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MacroLab Documentation
MacroLab: The Model
1
1 System Dynamics Modeling Concepts
2
2 Overview of the Model
3
3 Model Behavior Compared with Textbook Reference Behavior Patterns 5
3.1 Productivity and Factors of Production
6
3.2 Market Economy Better than Command Economy
8
3.3 Government Improvement of Market Outcomes
9
3.4 Inflation vs. Unemployment
12
3.5 Money and Inflation
13
3.6 Gains from Trade
14
4 Model Behavior Compared with US Economy Reference Behavior Patterns
4.1 Five-Year Forecasts
19
5 Detailed Model Structure
21
5.1 Main Model
25
5.2 Labor Sector of Production Submodel
28
5.3 Capital Sector of Production Submodel
35
5.4 Productivity Sector of Production Submodel
40
5.5 Price Sector of Production Submodel
44
5.6 Income Distribution Submodel
47
5.7 Consumption Submodel
49
5.8 Government Submodel
53
5.9 Money Sector Banking Submodel
57
5.10 Monetary Policy Sector of Banking Submodel
63
5.11 Exchange Rate Submodel
72
5.12 The Value of Simulation
76
MacroLab: The Interactive Learning Environment
1 Layout and Navigation
2 Historical Lab
3 Experimental Lab
4 Sector Tutorials
5 Final Comments
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MacroLab: The Model 1
MacroLab: The Model
This project has addressed a research question motivated by an overarching goal of
improving undergraduates’ learning of macroeconomics. Various adaptations of the feedback
method have been tested in controlled experiments, and the results described in papers 2-5 are
promising, measured in terms of student preference and performance. Each simple feedback
model used in the experiments had a specific pedagogical purpose, and together they can be
considered a sample from the full model the author uses when teaching macroeconomics.
This chapter describes and explains the structure and behavior of that full model.
Model validation is the process of building justifiable confidence in a model (Forrester
and Senge, 1980). What justifies confidence—and, therefore, the validation techniques—
depends on the purpose for which the model is built (Forrester and Senge 1980, Sterman
2000, Barlas 1996). The purpose of the MacroLab model in its current form is strictly
pedagogical. The intent of this chapter, therefore, is to provide the reader with an
understanding of the model that is sufficient for deciding whether it is a suitable
representation of the market economy in the United States. Suitable, in this context, means
that the real-world counterparts to the components of the model—and their general
relationships—should resemble the U.S. economy described in standard textbooks, whether
in words or models. Suitable also means that the behavior generated endogenously by the
model’s structure is more or less consistent with the behavior described by standard
undergraduate macroeconomics textbook models—whether in narrative, diagrammatic,
graphical, or mathematical form. Even mainstream textbooks have more or less subtle
differences in their description of how a market economy performs, but mostly they reach
similar conclusions, and a suitable MacroLab model should do the same when its purpose is
to convey the consensus view of macroeconomic principles to undergraduates. In addition, a
very large variety of structure-behavior tests and extreme condition tests have been
performed, and some will be illustrated in the submodel section. Suitable also means that the
model’s behavior should more or less resemble the historical behavior of the real-world
system on which it is based; in this case, the US economy over the past quarter century.
What distinguishes MacroLab from conventional methods, however, is how the story of
economic structure and behavior is told. The first difference is the emphasis on dynamics
rather than static equilibrium conditions. How the economy changes over time in different
contexts is the behavioral question that students repeatedly encounter, and the time series
graph is the workhorse tool for studying both historical trends and simulated behavior.
Secondly, the structure of the economy is explained in terms of reinforcing and counteracting
feedback loops. Students are encouraged to “think in time” and envision patterns that unfold
and interact in reinforcing or counteracting ways with earlier trends, instead of focusing on
isolated cause-and-effect events. The feedback loop is the unit of analysis, and student
understanding of the source of dynamic economic behavior requires seeking, identifying, and
explaining relevant feedback structure in an economic system. Another distinction, as the
next chapter explains, is the interactive method of engaging students in vicarious construction
of the model and “test driving” the MacroLab simulator. The simulation experiences
reinforce the insights gained from studying feedback loops. In addition, small-scale student
participation in model-building seems to facilitate understanding of a larger model; moreover,
MacroLab: The Model 2
such participation may build respect for the scientific method and an appreciation for theory
building by economists.
In short, MacroLab provides students with a different conceptual lens through which to
view the structure and behavior of the economy. Students see an economy in motion that
more or less regulates itself through a web of feedback loops that are accessible to student
inspection. Also, students get to experiment with alternative market structures—including
those that emerge from various fiscal and monetary policy efforts aimed at improving market
performance. This chapter presents the system dynamics model that is the foundation for that
learning experience. The first two sections briefly illustrate the central concepts in system
dynamics modeling and provide an overview of MacroLab’s stock-and-flow structure.
Section 3 compares the model’s behavior with reference behavior patterns commonly found
in mainstream textbooks and uses feedback loop diagrams for the structural explanations.
The fourth section compares the model’s behavior with historical reference behavior patterns
to see if forecasts of some actual U.S. economic patterns are reasonable. The lengthy final
section provides details on the structure of the MacroLab’s submodels, including a complete
listing of equations.
1. System Dynamics Modeling Concepts
System dynamics models are used for studying and managing problems in complex
feedback systems. Standard works include Forrester (1961), Richardson & Pugh (1989), Ford
(1999) and Sterman (2000). The conceptual building blocks for such models are stocks,
flows, and feedback loops, generically illustrated in Figure 1. A stock is an accumulation of
material or information. A net flow is the rate of change in a stock. The feedback loop
transmits information about the state of the system from the stocks to the decision rules—the
equations— that govern the flow, which then updates the stock and closes the loop. System
dynamics models are systems of differential
flow
equations. Typically non-linear and without
stock
analytic solutions, they rely on numerical
integration to generate simulated behavior. See
feedback
loop!
Sterman (2000, chapter. 6 and 7 and Appendix
A) and Ford (1999, chapter 3). Thus, the initial
Figure 1. Stock, Flow, & Feedback
value of the stock changes as the stock
Central Concepts in System Dynamics
integrates the net flow.
Figure 2 presents a more general version of a generic feedback system based on system
dynamics concepts. Complex systems such as an economy contain many stocks that interact
endogenously; that is, they have feedback effects on each other. All models have boundaries
(defined by the model’s purpose, level of aggregation, and time horizon) beyond which
exogenous influences originate, but those influences do not receive any feedback effects from
the model during the time horizon under study. In addition to the rectangles, pipelines, and
arrows that represent stocks, flows, and information links, the generic diagram also includes
small circles that represent endogenous auxiliary variables (with values determined by
equations) and exogenous parameters (with fixed estimates of values).
MacroLab: The Model 3
problematic gap
between desired
and actual condition
actions designed
to close the gap
desired
system
condition
time delay
in closing gap
net change
in system
condition
Actual
System
Condition
exogenous
influences
Other
Endogenous
Influences
net changes in other
endogenous influences
Figure 2. Generic Feedback System
The conditions of some stocks are managed (with varying degrees of success) by
agents in the system. In those cases, some desired conditions for the stocks are periodically
compared with actual conditions and, if problematic discrepancies (“gaps”) exist, corrective
actions are taken. Forming human perceptions of such gaps, making decisions on how to
close them, and then taking action are all time-consuming processes. The time required by
the feedback loop process—from stock to flow and back to stock—is an important
determinant of the system’s behavior.
2. Overview of the Model
The MacroLab system dynamics model consists of dozens of stocks and hundreds of
equations. Figure 3, however, displays a simplified version of the structure of the main
model. For purposes of clarity, the diagram shows only those information links that connect
the model’s real sector (bottom) with its nominal sector (top), also referred to as the “supply
side” and “demand side,” respectively. Nominal dollars flow through the demand sector,
while the real quantities flow through the supply side. In the middle of the diagram, part of
the nominal income generated by the supply side is divided among households, governments,
and businesses on the demand side. On the far right, the nominal aggregate demand is the
sum of demand-side spending by households, governments, and businesses, plus net exports,
and that nominal quantity is converted to real aggregate demand on the supply side. Unless
indicated otherwise, all variable values are determined endogenously by feedback within the
system. The diamond-shaped icons are linked to submodels, described in detail in section 5.
MacroLab: The Model 4
Figure 3. Simplified High-Level View of MacroLab Stock-and-Flow Structure
The production submodel determines the stocks of labor and capital to be employed
and acquired. A link not shown in Figure 3 connects capital acquisition decisions in the
production submodel to investment spending on the demand side. Changes in total factor
productivity (“productivity of labor and capital”) are based on exogenous growth rate
assumptions. The GDP equation is a Cobb-Douglas production function. The average price
level—the price index—is also determined within the production submodel, based on the
expected demand for goods and services and expected costs of production. The income
distribution submodel divides the nominal national income among households (“wages &
dividends”), government (“taxes”), and business (retained earnings, or “business saving”).
The consumption submodel determines household spending (“consumption”), which is
equal to most of disposable income (“wages & dividends” plus “transfer payments”)
received by households; the remainder is defined as saving (“personal saving”). Investment
spending, as noted above, is determined by capital acquisition decisions in the production
submodel. Note, however, that the source of funds for investment is the stock of savings,
which accumulates personal saving, business saving, government saving (usually a negative
value in the US, when government is usually borrowing rather than saving), and saving from
the rest of the world (usually positive in the US).
The government submodel receives taxes, makes transfer payments to households, and
makes purchases of goods and services from business firms. When government spending
exceeds tax revenue, government “saving” is a negative flow; i.e., government borrows from
the stock of savings. The government submodel also accounts for government debt, and
interest payments are included in transfer payments.
MacroLab: The Model 5
The banking submodel accounts for monetary flows between stocks of bank deposits
and currency held by the public, as well as flows to and from bank reserves. The reserves
are managed within the submodel according to the fractional reserve requirements
established by the central bank, the Federal Reserve System. Interest rates are also
determined within the banking submodel, based on the supply and demand for loanable
funds and the monetary policy established by the Federal Reserve. A single market interest
rate (not shown in Figure 3) is an output of the banking submodel, and the interest rate is an
input to both the consumption submodel and the production submodel, where it affects
consumer spending and capital spending (investment).
The foreign submodel—called the “rest of the world” or just RW—is literally a clone
of the domestic main model and all of its submodels. The purpose of the RW sector is to
enable demonstration of some interactive effects between two economies that trade with each
other. As a clone, its default parameter settings are identical to the domestic sector, but
parameters in both sectors are easily modified with the simulator controls in the interactive
learning environment (described in chapter 8). The two economies are linked by the flows of
trade (green inflow and outflow to the business firm stock of money) and flows of financial
capital (“RW saving in the US”—the green net inflow to the US savings stock). There is
also an exchange rate submodel that is accessible from the main model of the foreign sector,
and conversions can be made between US dollars ($) and RW rollers (®) for purposes of
international trade and capital flows.
More details about the submodels, including stock-and-flow structure and a complete
listing of equations, are provided in section 5. Before examining more structure, however,
the next step in building understanding of the MacroLab model is to compare its behavior
with reference behavior patterns drawn from mainstream macroeconomics textbooks.
3. Model Behavior Compared with Textbook Reference Behavior Patterns
In this section, the behavior of the MacroLab system dynamics model is compared with
reference behavior patterns illustrated or asserted in standard macroeconomics textbooks.
When teaching, the author uses both Mankiw (2007) and McConnell/Brue (2005)—
apparently the two best-selling economics textbooks in the United States (Beam 2005)—and
the reference behavior patterns have been selected from those two texts. For each behavioral
comparison, the structure of the MacroLab model is also presented, and the relationship
between model structure and behavior is explained.
Six of Mankiw’s (2007) “ten principles of economics” guided selection of the reference
behavior patterns.1 The list includes behavioral predictions based on Mankiw’s view of how
a market economy works. The principles are mainstream and are probably shared by most
economics textbook authors and a majority of other economists. In this section, therefore, we
use those principles to organize the discussion of MacroLab in the context of standard
textbook reference behavior patterns. Unless otherwise cited, all references pertaining to
those principles are taken from Mankiw (2007, chapter 1).
1
The other four are decision-making principles involving trade-offs, opportunity cost, marginal thinking, and
incentives that illustrate economic system structure rather than economic system behavior.
MacroLab: The Model 6
3.1 Productivity and Factors of Production. The first reference behavior pattern to
be examined is suggested by Mankiw’s assertion that “a country’s standard of living depends
on its ability to produce goods and services.” He associates standard of living with average
real income, and he emphasizes that productivity “is the primary determinant of living
standards.” He mentions that, historically, real per capita income in the United States has
grown about 2 percent per year, and he emphasizes that maintaining that rate doubles the
average income every 35 years. In chapter 7, Mankiw mentions the production function in
general terms, noting that output depends on the quantity and quality of the factors of
production and the prevailing technology. McConnell/Brue (2005, chapter 17) provides a
similar discussion of historical trends in productivity but does so in the context of an
aggregate supply and demand model, and then presents a specific simple production function
in which GDP equals the number of hours worked multiplied by the productivity of each
hour.
Panel A
Panel B
Figure 4. GDP Pattern due to Growth in Productivity and Factors of Production
Textbook Reference Behavior Pattern (A) and MacroLab Model Behavior (B)
Although neither textbook provides a times series graph that depicts output associated
with a specific production function, panel A of Figure 4 illustrates the behavior generated by
a generic adaptation of the McConnell/Brue production function. Generated by a spreadsheet,
the graph in panel A assumes 100 million workers at an initial productivity of $100,000 worth
of goods and services per year per worker. The overall growth rate was set at 3.5 percent,
with productivity accounting for 2.1 percent and workforce growth accounting for 1.4
percent. GDP doubled during the 20-year period, rising from $10 to $20.01 trillion per year.
Panel B shows the simulated behavior generated by MacroLab after adapting the growth rate
assumptions to the model. Simulated GDP at the end of 20 years was $19.39 trillion. The
estimates are quite close, but exploring the reason for the difference is instructive.
In standard textbook illustrations of the production function implicit in the spreadsheet
model (based on the McConnell/Brue production function), the growth rates are the assumed
ex post values. If the number of people working grew annually at a 1.4 percent rate and their
productivity grew by 2.1 percent, then total output would approximately double in 20 years
(since, by the rule of 70, 70/(1.4+2.1) = 20).
The initial condition assumptions were the same for both MacroLab and the spreadsheet
model (e.g., initial workforce size and productivity). The slight difference in 20-year GDP
estimates (20.01 and 19.39 for the spreadsheet and MacroLab, respectively) is due
differences in the implementation of the growth rate assumptions. In MacroLab, the
MacroLab: The Model 7
assumption of a 1.4 percent exogenous growth rate for the “workforce” is applied to the
“working-age population.” As the population grows, 70 percent of the new working-age
adults are assumed to be seeking employment. Thus, the spreadsheet assumption of 1.4
percent growth rate in employment is implemented indirectly in the model, via the growth in
the working-age population, the labor force participation rate, and, ultimately, the number of
workers who actually get hired (based on the demand for labor). How long it takes for a 1.4
percent growth rate in the working-age population to translate into a 1.4 percent growth rate
in employment depends on the structure of the model, just as it would depend on the structure
of a real economy. By the end of the 20-year simulation, employment had risen to 124.9
million. A 24.9 percent increase over 20 years reflects an annual growth rate of about 1.1
percent.
The spreadsheet model assumes the annual 2.1 percent growth in productivity is
output per worker. In MacroLab, the exogenous productivity growth rate refers to total factor
productivity, and is interpreted as a “technology” influence on the productivity of the factors
of production (labor and capital), rather than an assumption of the output per worker. The
capital-to-labor ratio is determined endogenously in the model, with the resulting mix of the
two factors influencing production via the Cobb-Douglas production. Thus, annual output
per worker rose from $100,000 to $155,242. A total percentage increase of 55.242 percent
over 20 years implies an annual growth rate in output per worker of 2.2 percent. Thus, the ex
post values of the growth rate in workforce were 1.1 percent and 2.2 percent for workforce
and workforce productivity, which would imply doubling the GDP in about 21 years instead
of 20 years, which is what MacroLab did.
Panel A
Panel B
Figure 5. Combination of Feedback Loops that Increase Labor and Capital Endogenously
after Stimulation by Exogenous Growth in Population & Productivity
The feedback loop diagrams in Figure 5 can be used to illustrate how the model’s
structure generated changes in the employed labor stock from two directions. First,
multifactor productivity growth increases GDP immediately. As GDP grows, wages increase,
giving a boost to both consumption and personal saving. The growth in consumption (part of
aggregate demand) encourages more employment. The second effect on labor follows a path
through wages. The growth in wages due to rising GDP constrains somewhat the growth in
employment. However, the labor force is initially growing faster than the number of new
jobs, and the pressure of initially rising unemployment keeps wages from rising as much as
MacroLab: The Model 8
they would have otherwise. Thus, employment and the unemployment rate are both rising at
first. After labor demand grows to fully reflect the new product demand conditions, the
unemployment rate stabilizes. As Figure 5 shows, capital grows endogenously after
investment is stimulated by rising aggregate demand and falling interest rates. The CobbDouglas production function (GDP equation) transforms the growth in productivity, capital,
and labor into an average annual GDP growth of slightly more then 3.3 percent, causing it to
double in the twenty-one years.
3.2. Market Economy Better Than Command Economy. The second Mankiw
principle is that a market economy usually produces better results than a command economy.
He emphasizes that the price mechanism is the instrument used by Adam Smith’s “invisible
hand” to direct economic decision-making by consumers and producers, and that when
“government prevents prices from adjusting naturally to supply and demand, it impedes the
invisible hand’s ability to coordinate the millions of households and firms that make up the
economy.” To test MacroLab’s conformance with this principle, a hypothetical reference
behavior pattern was generated under the assumption that government price controls are in
place, contrary to a key principle of a market economy. We might assume that the
government policy is premised on the belief that any price changes that occur quickly are
harmful and should be avoided. Thus, the government’s price control policy goal will be
assumed to apply to both price increases and decreases. Price increases might be controlled
to protect consumers, while price decreases might be controlled to protect small businesses
from predatory pricing by large-volume competitors. Specifically, in this fictional price
controls program, assume that (a) all price changes in the economy require advance
government approval, (b) businesses must provide one year’s worth of data to justify
changes, and (c) permissible changes must be implemented gradually over a one-year period.
In other words, price changes would occur very slowly and only after government approval.
The behavior of an economy under such controls can be simulated in MacroLab and
compared with a market economy in which prices respond “naturally” to changing demand
and supply conditions. Blinder’s (1997) survey suggests that price managers wait, on the
average, about three months before changing prices after observing changes in market
conditions. Even such “sticky” prices would respond more quickly than prices controlled
under the government
program outlined above.
For purposes of the
simulation experiment, we
assume the three-month
delay is “natural” and that
the economy is in
equilibrium until an
exogenous
shock
permanently reduces
consumption spending by
about 2 percent (i.e., the
average propensity to
Figure 6. Unemployment Rate Response to Permanent
Decline in Average Propensity to Consume, with and
consume declines to a lower
without the “delayed” price controls
percentage permanently).
MacroLab: The Model 9
Figure 6 compares the consumption shock effect on the unemployment rate under the
government price controls program (black) and in a free market (red). Clearly, given this
shock to the model economy, more stability is provided by the market than by the
government. The feedback loop diagram in Figure 7 is based on the MacroLab stock-andflow structure responsible for these simulation results. Loop R1, the main reinforcing loop in
the economy, amplifies the effect of falling aggregate demand triggered by the consumption
shock. Less production (GDP) reduces wages, which reduce consumption, thus pushing
aggregate demand even lower. Declining demand contributes to an undesired inventory
increase, which should put downward pressure on prices. When prices are slow to respond
(in this case, due to government’s price control program), the counteracting effect of loop C1
is weak, and aggregate demand continues to fall under the reinforcing pressure of loop R1.
Meanwhile, labor demand continues to fall and unemployment rises, due to the reduction in
product demand and the inventory surplus (loop C2). The rise in the unemployment rate
should put downward pressure on nominal wages and prices. If there is a sluggish response
of prices to falling wages, however, it takes longer for prices to drop and encourage a
recovery in demand (loop C4). In general, then, the slower that prices respond to changes in
demand and supply conditions, the longer the unemployment trend will continue after it is set
in motion (in either direction). The simulated price controls program illustrates the
unintended consequences of government-mandated sluggish prices.
Figure 7. Feedback Loops that Influence Price Response
to a Consumption Shock
3.3 Government Improvement of Market Outcomes. Mankiw also emphasizes that
“the invisible hand can work its magic only if government … maintains the institutions that
are key to a market economy.” His discussion focuses on protecting property rights,
promoting competition, and correcting market failures due to externalities. Implicit in this
third principle, however, is that government has a responsibility to continuously review its
own policies and avoid undermining widely-held economic policy goals such as economic
growth, price stability, and high employment. In short, economic policy criteria should be
part of any assessment of government policy, and government policies should be modified if
doing so would improve market outcomes, ceteris paribus. Even if other things were not
MacroLab: The Model 10
equal, potential economic policy benefits of government policy changes should be weighed
against potential costs. Government budget policy provides an example. When Mankiw
(2007, ch. 18) considers the pros and cons of balanced budgets, he cites the following
common rationale for a budget deficit during a recession:
It is reasonable to allow a budget deficit during a temporary downturn in
economic activity. When the economy goes into a recession, tax revenue falls
automatically, because the income tax and the payroll tax are levied on measures
of income. If the government tried to balance its budget during a recession, it
would have to raise taxes or cut spending at a time of high unemployment. Such a
policy would tend to depress aggregate demand at precisely the time it needed to
be stimulated and, therefore, would tend to increase the magnitude of economic
fluctuations.
A quick illustration of Mankiw’s example is provided by extending the previous
simulation experiment. In the previous experiment, one structural assumption was not
mentioned; namely, that government balanced its budget. The curves in Figure 6 were
generated with a MacroLab assumption that government followed this balanced budget
decision rule: When national income changes, tax revenue changes immediately, and
government spending gradually adjusts up or down to the new inflow of tax revenue. There
would be very brief cyclical surpluses or deficits, lasting only until the government balanced
the next year’s budget. An alternative policy is a so-called unbalanced budget decision
rule: When national income rises, tax revenue rises immediately, and government spending
gradually adjusts upward to match the higher flow of tax revenue. When tax revenue falls,
government spending does not change. Under such a policy, there would be brief budget
surpluses when tax revenue rose, lasting only until government could find a way to spend the
money. Cyclical deficits, however, would last longer, since deficit spending would continue
until tax revenue regained an inflow rate that matched the “frozen” spending outflow rate.
The shortfall would be covered by deficit spending, which would raise the government debt.
Figure 8. Deliberate Deficit Spending Results in a
Quicker Economic Recovery
In Figure 8, the blue curve illustrates the effects of an unbalanced budget policy on the
unemployment rate. The marginal benefit of deficit spending is smaller than the impact of
ending the price controls program. Yet, a somewhat quicker recovery does occur when the
MacroLab: The Model 11
balanced budget policy is abandoned. Whether the benefits of deficit spending outweigh the
costs is an empirical question, and the answer will vary case by case. Searching for the
source of potential costs, however, is facilitated by the feedback loop “map” in Figure 9
(which omits business taxes and business saving from the picture, without affecting the point
of the example).
Figure 9. Additional Upward Pressure on
Demand, Prices, and Interest Rates
due to Government Deficit Spending
In Figure 9, focus on the heavy blue links that map three effects of deficit spending—on
aggregate demand, prices, and interest rates. When nominal taxes fall in the aftermath of the
exogenous investment shock, government spending continues at its previous rate. Initially,
additional aggregate demand (that brings the unemployment rate down more quickly in
Figure 8) comes from consumption, since the fall in taxes means that disposable income does
not fall as much as total income. Eventually, that encourages more investment. The
additional aggregate demand, however, puts upward pressure on prices. Thus, prices are
expected to be higher when deficit spending occurs. The higher prices, in turn, negate some
of the real aggregate demand growth expected from the deficit spending policy. Finally, since
government spending exceeds tax revenue, financing the deficit reduces the stock of national
savings and puts upward pressure on interest rates. When interest rates rise, that constrains
the growth in both consumption and investment that could have been expected from the
deficit spending policy.
The net effect of the deficit spending policy in this MacroLab simulation exercise was
expansionary. Real aggregate demand grew a little faster, and the unemployment rate fell a
little faster, compared to the behavior under the balanced budget policy (Figure 8). The
simulation results revealed that, compared to the situation when a balanced budget policy was
in effect (red curve in Figure 8), deficit spending pushed prices about 10 percent higher and
interest rates almost a full percentage point higher by the end of the simulation period.
Government debt and interest payments grew substantially. Interest payments on the
government debt grew from 12 percent of total government spending to 18 percent. With
total spending flat, the extra debt service spending went to transfer payments and government
spending on goods and services was reduced. Comparing a policy benefit (e.g., lower
MacroLab: The Model 12
unemployment) with a policy cost (e.g., higher prices) raises an issue that is central to the
next Mankiw principle.
3.4 Inflation vs. Unemployment. Mankiw (2007) and McConnell/Brue (2005) agree
that there tends to be a “short-run” trade-off between inflation and unemployment.
According to Mankiw (p. 13), “Over a period of a year or two, many economic policies push
inflation and unemployment in opposite directions.” Writing more precisely, McConnell/
Brue, (p. 197) define the short run as “a period in which nominal wages (and other resource
prices) do not respond to price-level changes” and emphasize that the short run is “not a set
length of time such a one month, one year, or three years.” The point that both textbooks
make, however, is the consensus view among economists that opposite-direction movements
between inflation and the unemployment rate are not sustainable, and that the so-called
Phillips curve is downward sloping in the short run and vertical in the long run as Friedman
(1968) argued forty years ago (Mankiw, 2007, ch. 17). Mankiw (2007, ch. 17) documents
how the graphical aggregate supply and demand (AS/AD) model accounts for the short-run
phenomenon when the AS curve is upward sloping and how the long-term disappearance of
the trade-off follows from assuming a vertical AS curve. Earlier (p. 13), he describes the
short-term scenario in simple terms, given the assumption of higher aggregate demand for
goods and services:
Higher demand may over time cause firms to raise their prices, but in the
meantime, it also encourages them to increase the quantity of goods and services
they produce and to hire more workers to produce those goods and services.
More hiring means lower unemployment.
To test MacroLab’s consistency with this principle, the model economy was subjected
to a step increase in bank reserves amounting to $40 billion, which then “multiplied” to a
number almost ten times that amount. The trade-off between inflation and unemployment
after the increase in the money supply is displayed several ways in Figure 10. The top-left
panel shows the standard time series graph, where inflation (red) moves (with a lag) in a
direction that is generally opposite to the direction of the unemployment rate (blue), thus
illustrating the trade-off expressed in Mankiw’s principle.
To explore this issue further, consider the bottom-left panel, where inflation is plotted
on the vertical axis, the unemployment rate is on the x-axis, and the overall pattern of the
black line (drawn over time during the simulation) suggests a downward sloping “Phillips
curve.” The panel on the bottom-right of Figure 10 tells a quite different story about the
Phillips curve, based on a considerably different time series graph in the top-right panel. The
difference in the two simulation runs is the assumption about how quickly wages adjust to
changes in employment conditions. The nominal wage equation in MacroLab is influenced
by changes in the unemployment rate but not immediately, and variation in the adjustment
time is responsible for the variation in the trade-off between inflation and unemployment in
Figure 10. On the left, the adjustment time is very quick—one month. On the right, the
adjustment time is two years. The default assumption in MacroLab is three months, but the
two extreme values were used to reveal a striking contrast in behavior. Similar variations in
behavior result from variations in the average adjustment time for prices, and also for the
average time taken to adjust wages when prices change.
inflation
inflation
MacroLab: The Model 13
unemployment rate
unemployment rate
Figure 10. Variations in Trade-Off Between Inflation and Unemployment Rate
Time to Adjust Wages to Unemployment Rate: (left) One Month (right) Two Years
The pattern of real-world, empirically observed data on inflation and the unemployment
rate could be due to delays inherent in the price/wage/unemployment adjustment processes,
and not due to fundamental changes in those relationships. In the bottom-right panel of
Figure 10, for example, the equation (the mathematical structure of the relationship) did not
change. The adjustment time did not change; it was a constant two years. Yet, depending on
when an observation was made, inflation and unemployment might appear to be inversely
related, positively related, or not related at all! A so-called “long run” vertical Phillips curve
would be consistent with the same empirical data, but that concept implies that there is some
future period when equilibrium reigns and inflation and unemployment are no longer in a
process of adjustment. The dynamic behavior in Figure 10 seems more consistent with a
world in which the “long run” is nothing more than a series of short runs.
3.5 Money and Inflation. Mankiw’s fifth principle is that “prices rise when
government prints too much money.” Concurring, McConnell/Brue (2005, ch. 19) note that
“mainstream economists agree...that excessive growth of the money supply is the major cause
of long-lasting, rapid inflation.” This principle has its origin in the quantity theory of money
(Fisher 1911), but owes it modern consensus status to the work of Milton Friedman, whose
best known (1963) summary is, “Inflation is always and everywhere a monetary
phenomenon.” To test MacroLab’s conformance with the behavior implicit in Mankiw’s fifth
principle, the money stock (M2) received a simulated injection of $40 billion, on top of an
initial equilibrium value of $4.0 trillion. The results are shown in Figure 11, and it is clear
that prices rise at about the same rate as the money supply, which is consistent with the
quantity theory of money (Mankiw, ch. 12). The different patterns in the two panels in
Figure 11, however, deserve close attention.
MacroLab: The Model 14
Implicit textbook assumption: Money Supply Grows
Quickly after Increase in Reserves
MacroLab assumption: Money Supply Grows Only as
Fast as the Growth in Loan Demand
Figure 11. Prices Will be Higher After Money Supply Rises, but the transition pattern
depends on whether (left) banks can lend most of their reserves soon after the shock or
(right) they must wait on demand for loans to grow.
The standard textbook explanation of the response of the banking system to an injection
of reserves by the central bank is implicit in the behavior on the left panel in Figure 10. All
of the initial supply of excess reserves would be converted to loans quickly, and the new
deposits resulting from the loans would create additional reserves for lending as the “money
multiplier” process gained steam. In that case, there would be a quick rise in the money
supply and a gradual adjustment to the new goal that is implicit in the parameters of the
model (reserve ratio, currency-to-deposit ratio, etc.). The red pattern on the left resembles a
simple first-order delay adjustment to a goal (because it is). The default assumption in the
banking submodel of MacroLab, however, is that bankers cannot lend a sudden glut of new
reserves as quickly as they might desire. Borrowers have to be interested in taking out new
loans. To promote that interest, banks can lower interest rates. Those are the steps in the
process followed by the model, reflected in the red curve in the right panel of Figure 11.
When interest rates start falling, both consumers and businesses respond gradually, but the
full money supply expansion eventually occurs (in this simulation experiment where nothing
else happens that might derail the expansion).
3.6. Gains from Trade. The last Mankiw principle we consider for model testing is
that “trade between two countries can make each country better off.” The point is made
somewhat differently by McConnell/Brue (2005, ch. 6): “Specialization and international
trade increase the productivity of a nation’s resources and allow for greater total output than
would otherwise be possible.” The foundation for textbook explanations of the incentive for
trade is the principle of comparative advantage (Mankiw 2007, ch. 13, and McConnell/Brue
2005, ch. 20). As explained in section 2, however, the current version of MacroLab’s foreign
submodel (RW) is a clone of the domestic model. As such, there are no explicit “specialties”
produced by the respective US and RW sectors. The current version of the model contains no
mechanism for productivity growth due to specialization; thus, simulations will not show the
two economies emerging over time as a result of the comparative advantage principle. We
should not expect the kind of “gains from trade” explained by textbook illustrations of
country A and country B—previously engaged in inefficient attempts at self-sufficiency—
suddenly finding that each has an unexploited comparative advantage that trade can exploit.
The lack of such structure means the lack of such behavior. In short, the US and RW have no
structural incentive to trade with each other. That is a weakness in the current open economy
MacroLab: The Model 15
version of MacroLab that will be addressed in future versions. Nevertheless, if trade occurs
(triggered by an exogenous flipping of a switch in the model) then the resultant endogenous
behavior of MacroLab is consistent with a broad range of textbook behavioral descriptions of
open economy macroeconomics. This section compares the behavior and structural
explanations of both, in an effort to provide the reader with confidence that similar behavior
occurs for similar reasons. In contrast with previous sections, however, the explanation of
structure precedes the view of behavior.
To begin, review Figure 3 (in section 2) for a review of MacroLab’s main model for the
US sector. Note, on the nominal side, the green two-way flows connecting the US sector
with the RW sector. Payment flows for trade (imports and exports) connect with business
firms, and financial capital flows link with the national savings stock. The RW main model is
structurally identical. Figure 12 shows the relevant excerpts from the two main models.
Adjusted by the exchange rate (not shown), the outflow of US import payments equals the
inflow of RW export receipts, and the inflow of US export receipts equals the outflow of RW
import payments. The nominal net exports are converted to real quantities when added to
real aggregate demand. The financial capital flow is a net rate, and the net saving by the RW
in the US is equal to the negative value of net saving by the US in the RW (again, adjusted by
the exchange rate). These are structural representations of textbook definitions of exports,
imports, and financial capital flows.
US Sector
RW Sector
Figure 12. Nominal Inflows to US Sector are Nominal Outflows from RW Sector
and Nominal Net Exports are Converted and Added to Real Aggregate Demand
With the textbook consensus as guidelines for structuring open economy relationships,
examine the diagram in Figure 13, which provides a high-level overview of most of the
feedback structure in MacroLab’s open economy. (Financial capital flows are added later,
and a fourth influence—speculation by traders in international currency markets—is not part
of the model’s structure.) The two sides of the diagram are mirror images of each other—
with the US sector on the left and the RW sector on the right. The open economy diagram
illustrates for students how the fortunes of trading nations rise and fall together. The heavy
red curve traces a not-so-obvious reinforcing feedback loop that connects aggregate demand
in the US with aggregate demand in the RW. An increase in US aggregate demand increases
MacroLab: The Model 16
US imports and raises RW aggregate demand, which then causes an increase in RW imports
(US exports) and an increase in US aggregate demand.
Recall the caveat about the economies being clones. When the foreign submodel is
activated, the two economies “trade” with each other, but the overall behavior should
resemble the expected behavior of two trading partners that are twins. The default settings
for MacroLab assume that the US and RW clones are identical in every way, including initial
stock values, and that they follow the same decision rules. For example, both spend ten
percent of nominal national income on imports when the foreign sector switch is ON.
Initially, the model is in equilibrium and both sectors have zero net exports.
US sector
RW sector
Figure 13. MacroLab Open Economy Feedback Structure
(without exchange rate sector)
MacroLab: The Model 17
To conduct the behavior test, we conducted four simulation experiments under different
assumptions about productivity growth and interaction between the US and the RW.
• In the first simulation, both the US and RW began with equal productivity
growth rates (1.0 percent annually), but the US technology received a positive
shock (productivity increased permanently to 2.0 percent) in year five. There was
no trade between the sectors, and the technological progress was confined to the
US sector.
• The second simulation differed from the first only by enabling trade between the
US and RW economies. The technological jump in productivity was still confined
to the US sector.
• During the third simulation, the US and RW are still engaged in trade. In
addition, technological progress spreads beyond borders freely at a slow rate.
Thus, after the step increase in US productivity, the RW “learned and applied” the
same innovations. RW productivity growth accelerated until it matched the US
rate. The process was slow, however, taking almost 15 years for full adjustment.
• The last simulation was identical to the third, except for a more rapid transfer of
technology. Only a six-year period was needed for RW productivity to regain
parity with the US.
1st Simulation
Trade
2nd Simulation
no
US productivity
growth
3rd Simulation
4th Simulation
yes
1% in years 0-4 and 2.0% thereafter
RW productivity
growth
1% every year
1% every year
1% in years 0-4 and
rises slowly to 2.0%
1% in years 0-4 and
rises quickly to 2.0%
US GDP
by year 25
$17.1 trillion/yr
$16.8 trillion/yr
$17.0 trillion/yr
$17.1 trillion/yr
RW GDP
by year 25
$13.5 trillion/yr
$13.8 trillion/yr
$16.1 trillion/yr
$16.7 trillion/yr
Total GDP
by year 25
$30.6 trillion/yr
$30.6 trillion/yr
$33.1 trillion/yr
$33.8 trillion/yr
Figure 14. Tests of the Gains-from-Trade Principle
Figure 14 summarizes the four tests, and the results are graphed in Figure 15. A
comparison of the first and second simulation results suggests a mere redistribution of
income rather than “gains from trade.” That is not surprising since, as we have discussed,
the structure of the model does not provide the US and the RW with comparative advantages
in production. Merely “causing” trade by an equation that makes imports proportional to
national income is not the same as building incentives for trade. Indeed, if two real-world
economies were truly twins, there would be no incentive for trade. So, in a sense,
simulations 1 and 2 illustrate the special case when trade is a zero-sum game.
MacroLab: The Model 18
However, it would be easy for students to misinterpret a comparison of the first two
simulations. As a practical pedagogical experiment, it should be deferred until the model can
be restructured to reflect the comparative advantage principle. At that time, a series of trade
experiments “with” and “without” structural comparative advantage may have a powerful
instructional impact. On the other hand, the impact of the technology transfer speed could be
a useful learning exercise for students at the present time. Assume the 2nd simulation is the
base case: trade occurs but the RW is stuck with its original productivity growth rate. As
technological progress spreads, both economies grow, and the faster the technology transfers,
the more both economies grow. That is an important manifestation of the gains-from-trade
principle.
1st Simulation (no trade)
2nd Simulation (trade; no technology transfer)
3rd Simulation (trade; slow technology transfer)
4th Simulation (trade; fast technology transfer)
Figure 15. Results of Gains-from-Trade Simulation Experiments
Can MacroLab replicate the textbook behavior implicit in the claim that trade between
two countries will make each country better off? The answer is no, because such a claim
relies on the assumption that trade will not take place unless both countries have a
comparative advantage in producing some good or service. For reasons previously
explained, that assumption does not apply to nations that are identical twins such as the US
and RW sectors in MacroLab. However, both the feedback structure and the simulator
enable students to see and experience the reinforcing structure and behavior that tie together
two market economies that trade freely with each other. If “gains from trade” is interpreted
more broadly to mean the US economy benefits when its trading partners are growing
strongly, then the current version of the model illustrates the principle and does so for the
right reasons.
MacroLab: The Model 19
4. U.S. Economy Reference Behavior Pattern compared to MacroLab Behavior
Sterman (2000) cautions against using any models for unintended purposes, and the
primary purpose of the MacroLab model is to facilitate student understanding of
macroeconomics rather than forecast economic trends. Like most models, it aims for the
right balance between simplification and realism. However, since MacroLab is a simulator
and students get to “test drive” the model economy during the course, credibility of the
learning experience depends somewhat on the data generated by the model. That puts a little
more emphasis on realism than would be the case with most teaching models. Although
MacroLab was not built for the purpose of tracking historical trends or forecasting future
trends in the economy, its structure should generate behavior that is more or less consistent
with observed behavior in a real economy. To the extent that it is capable of doing so,
credibility should rise among students and also among instructors interested in the model.
With Sterman’s caveat in mind and the reader forewarned that “MacroLab is Not Designed
for Forecasts,” this section provides some data that may be of interest to those who use the
model in an instructional setting.
Each year, the U.S. Congressional Budget Office (CBO) provides members of Congress
with an updated assessment of the accuracy and precision of the five-year economic forecasts
that the agency has been generating since 1976. The forecasts are, of course, compared with
actual behavior in the U.S. economy. More importantly for our purpose here, the CBO
forecasts are also regularly compared with forecasts originating in the Administration (the
President’s annual budget report to Congress, since 1976) and in the private sector (the socalled Blue Chip consensus forecast of about fifty economists, since 1979). Thus, the report
is a rich source of historical forecasts from three prominent forecasting bodies. In this
section, we compare MacroLab’s “forecast” of gross domestic produce (GDP) since 1979
with the forecasts coming from CBO, the White House (WH), and the Blue Chip economists
(BC).
The forecasts from CBO, WH, and BC are not released simultaneously, but they are all
released during the first quarter of the first year of the five-year forecast period (e.g., during
January, February, or March of 1979 for the five-year period from January 1979 to December
1983). The CBO, WH, and BC forecasts were actually GDP growth rate forecasts, which
have been transformed to GDP values by applying those growth rates to the GDP at the
beginning of each forecast period. The trend line for actual GDP (black) in Figure 16 is based
on fourth quarter data for the year indicated, and the forecasts at that same point were made
during the first quarter five years earlier.
The MacroLab “forecasts” were simulation runs over successive 5-year horizons,
beginning with the first quarter of 1979, and actual historical data initialized the material
stocks at the beginning of each run. The annual working age population growth rate was set
at a constant 1.2 percent. For simulations starting in 1979-1985, 1986-1999, and 2000-2001,
the multifactor productivity growth rate was set to 0.8, 1.1, and 1.5 percent, respectively.
Those average productivity growth rates would have been observed over the five-year period
preceding the respective forecasts and represent an assumed continuation for the next five
years. In addition to the productivity growth rate, there were two other variable exogenous
inputs—desired inventories and net foreign flows of payments and capital. Since 1980,
MacroLab: The Model 20
inventory-to-final sales ratios have been declining at about a 2 percent annual rate, but that
would have been unknown future data to any of the forecasters (and to MacroLab).
However, anticipation of such declines over an upcoming five-year forecast period could be
provided by observing past five-year trends. Thus, the estimate for desired inventories was
formulated as a third-order delay with an average delay of five years. Likewise, the exact
trend of net exports payments and foreign capital flows would not be knowable in advance,
but could be estimated by forecasters using prior information; again, a third-order delay
formulation was used with an average delay of five years. Given these settings, the equations
in the model produced continuous estimates of GDP over a five-year period, with the final
estimate entered as the “five-year forecast” for the end of each year in Figure 16.
Figure 16. GDP Forecasts for Years Ending 1983-2005
Based on Forecasts made Five Years Earlier
Sources for external forecasts and data: CBO’s Economic Forecasting Record, Congressional Budget Office (November
2006) and Bureau of Economic Analysis, NIPA Tables, Table 1.1.5, Gross Domestic Product.
Various statistical procedures could be used to estimate the “best” forecast but that is
not at issue here. Visual inspection makes clear that MacroLab produced a series of five-year
forecasts that is at least “respectable” when compared with the forecasts of three prominent
forecasting bodies in the United States.
MacroLab: The Model 21
5. Detailed Model Structure
Earlier, when overall model behavior was demonstrated, feedback loop diagrams
were used to provide explanatory insight into the model structure responsible for the
behavior. The purpose of this section is to give readers a better grasp of the structure and
behavior of each sector of MacroLab and to clarify the connections between sectors. In
addition to providing sector-by-sector analyses, this section also aims to reinforce readers’
accurate preliminary impressions or correct any misperceptions that may have formed when
viewing overall model behavior in the first half of this chapter. Each subsection is devoted to
a single sector and provides a stock-and-flow diagram and an annotated list of equations.
There are also demonstrations and explanations of stand-alone behavior of individual
submodels. Here is a section guide:
Subsection
Topic
page
5.1
Main Model
25
5.2
Labor Sector in Production Submodel
28
5.3
Capital Sector in Production Submodel
35
5.4
Productivity Sector in Production Submodel
40
5.5
Price Sector in Production Submodel
44
5.6
Income Distribution Submodel
47
5.7
Consumption Submodel
49
5.8
Government Submodel
53
5.9
Money Sector in Banking Submodel
57
5.10
Monetary Policy Sector in Banking Submodel
63
5.11
Exchange Rate Submodel
72
Figure 17. Subsection Guide for Section 5
Equation Structure and Parameter Estimates. About 200 equations are discussed in
this section—about forty percent of the total. It is not necessary to examine nearly 500
equations to get a comprehensive view of the model structure at the equation level. For
example, it would be repetitious to examine the 170 equations in the foreign sector since it is
a clone of the US sector. Most of the remaining equations are in the Data Sector, consisting
of initial values (e.g., initial GDP for experimental simulations), historical data (e.g., table
function displaying yearly historic M2 values), and miscellaneous calculations and
conversions (e.g., calculating inflation as the price index changes and converting nominal
values to real values). The final category not discussed consists of equations that implement
ON/OFF switch commands (e.g., to activate the foreign sector or to trigger an exogenous
money supply shock). Any equation not listed is available upon request.
About three-fourths of the equations reflect hypotheses about the structure of an
economy—how the pieces fit together, the incentives that give rise to decision rules, and the
decision rules themselves. Less than ten percent of the equations are definitional
MacroLab: The Model 22
relationships. The remainder (less than twenty percent) are exogenous parameter estimates—
numerical constants that provide quantitative detail to the basic structure and are presumed to
be unaffected by feedback within the model during the time horizon of a simulation run. For
example, the growth rate of the working-age adult population does not change radically from
year to year and is not likely to be affected by economic factors over the course of a business
cycle; thus, a constant value of that growth rate can be assumed, as it has in MacroLab. A
different formulation strategy would be necessary if the model were designed for long-term
economic development planning. In that case, since the population growth rate over many
decades might be influenced by economic growth rates, some structural feedback relationship
should be hypothesized. In its current form, MacroLab is what might be called a business
cycle model, appropriately used to study the economy over a period of several years rather
than several decades. That is why the comparison with a reference behavior pattern of the
US economy in section 4 was limited to five-year periods.
It is also important to remember that MacroLab was designed as a teaching model.
Generating accurate behavior patterns (for the right structural reasons) is more relevant than
achieving numerical precision when teaching and learning about the economy. Both qualities
in a model are desirable, of course. However, economics is often described as the science of
scarcity, and the allocation of time and effort when building a model is no less an
optimization problem than the allocation of labor and capital in a factory assembly line.
Therefore, relatively less effort in this modeling project has been devoted to parameter
estimation than would be done when developing a policy model seeking to replicate actual
problematic behavior and evaluate detailed policy options. Many of the parameter
assumptions, therefore, should be taken with the proverbial grain of salt. Or, striking a more
positive posture, MacroLab’s interactive learning environment provides students with
abundant opportunities to experiment with various plausible parameter assumptions. That
said, most parameters were estimated from available historical data, from published empirical
research, and from exemplary modeling work of others who followed a similar eclectic
strategy.
More important than the accuracy of a particular parameter is the degree to which the
performance of the model is sensitive to different values of that parameter. Sensitivity
analysis, therefore, is essential to establishing confidence in the overall model even while
acknowledging that some parameters are guesstimates. In the discussion of submodel
equations, special attention is given to the sensitivity analyses that have been conducted,
particularly those relating to estimates of time constants in delay formulations. Moreover, the
results of sensitivity analyses provide a prioritized research agenda for improving parameter
estimates.
Initial Values. The model can run in two modes: experimental and historic.
Primarily, the two modes differ in the way the stocks are initialized. In experimental mode,
the stocks always have the same initial values, the selection of which was guided by three
criteria. First, an effort was made to make their relative magnitudes historically realistic.
Second, the values had to initialize the model in equilibrium so that simulation results would
be easier to interpret. Constrained by the first two criteria for initial values, the third was to
use round numbers that students would find relatively easy to remember and manipulate (e.g.,
GDP = $10 trillion/year, M2 = $4 trillion, and the price index = 1.00).
MacroLab: The Model 23
In historic mode, stocks take on the initial values that existed in the particular historical
year in which the simulation begins (e.g., 1986, 1997, or 2001), and the model is simulated
from that initial disequilibrium state. After the simulation begins in historic mode, however,
stocks change endogenously based on the same equations used in the experimental mode.
Since historical stock data for the rest of the world are not included in the model, the foreign
submodel does not function in historic mode. Instead, the US sector relies on historical
exogenous values for U.S. imports, exports, and net capital flows.
Reading the Tables. Inspect Figure 18 before reading the various equation tables. It
contains excerpts from those tables, and getting acquainted with the format will make it
easier to understand the information in the tables later on. In the first column, each equation
has a number, and that facilitates subsequent reference to the equation in the text. To make it
easier to find the equations in the diagrams, the second column displays icons that indicate
whether the equations refers to a stock (rectangle), flow (arrow), or an auxiliary variable
(circle). An auxiliary variable icon containing a small square within a circle is a smooth
function; i.e., a delayed information stock.
Equation 90, for example, indicates that
“nominal dividends” is calculated by multiplying “business disposable income” by the
“dividends percentage,” but that the calculation is smoothed over an average time period of
one quarter (.25 years) since dividend payments are typically delayed beyond the end of the
accounting period. The third column displays the left-hand side of the equation (the equation
name), and the fourth column shows the right-hand side of the equation. The Runge-Kutta 4
integration method was utilized within the STELLA1 software, with the calculation interval
(dt) set to .005 years (one-fourth the length of the shortest adjustment time in the model— .02
years, or approximately one week).
An equation’s details may depend on whether the model is running in historic mode or
experimental mode. Sometimes, an equation includes an “IF/THEN” statement and takes one
value if the historic mode switch is ON and another if it is OFF. In other cases, it was more
convenient to multiply entire expressions by the value of the historic mode switch or its
complement (1-historic mode), thus making the irrelevant portion of the equation equal to
zero. Displaying the various conditional statements and associated nested parentheses would
make reading the equation lists unnecessarily difficult. Therefore, in the tables, such
equations have been simplified by separating and marking them to indicate which mode
would be running. Equation 26, for example, shows that the initial value for the Employment
stock is 100 (million) persons when the model is running in experimental mode. However,
when in historic mode, the initial value will be the actual historical number of employees in
the first year of the simulation time period. Equation 74 shows that the exogenous
multifactor productivity growth rate can be set arbitrarily when in experimental mode (E), but
a smoothed historical estimate can be used when in historic mode (H). Additional
simplification is achieved by removing all references to switches that regulate the conditions
under which the equations are calculated. For example, the equation for the “target Fed funds
rate” (in the list for the Monetary Policy Sector in the Banking Submodel) does not include a
reference to the “open market operations policy” switch, but that switch must be ON before
the “target Fed funds rate” will have any non-zero value. Unless indicated otherwise, dollar
1
STELLA is a registered trademark of isee systems (http://www.iseesystems.com).
MacroLab: The Model 24
amounts always refer to trillions, persons are measured in millions, and time is measured in
years.
The bottom row of each table lists right-hand side variables that are not defined in the
current table and indicates where those equations can be found. In Figure 7.23, for
illustration purposes, only one is listed—“operating surplus”—and that equation can be found
in the Income Distribution Submodel table. Finally, as an aid to navigation if a table overlaps
a single page, there is a descriptive label at the top and at the bottom of each table.
Equation Table Illustration
Left Side of Equation
1
GDP
26
Right Side of Equation
labor & capital * productivity of labor & capital
Employment(t - dt) + (net hiring) * dt
units
$/year
persons
Employment(t)
INIT historical = historic employment
INIT experimental = 100
74
multifactor productivity
growth rate %
90
nominal dividends
96
disposable business
income
operating surplus
H: smoothed historic productivity growth rate
E: 0
1/year
smth1(disposable business income * dividends pct,.25)
$/year
operating surplus - business taxes
$/year
Income Distribution Submodel
Figure 18. Illustrative Excerpts from Various Equation Tables in Section 5
MacroLab: The Model 25
5.1 Main Model
Figure 19. Main Model
Almost all of the equations at the main model level are determined at the submodel
level, discussed in the pages that follow. The exceptions are nominal aggregate demand (#5
in the equation list) and (real) aggregate demand (#4). A summary of the main model was
provided in section 2 and will not be repeated here. However, Figure 19 does show
additional links that were omitted from Figure 3. The link from the production submodel to
investment (#18) reflects the dependence of investment spending on capital acquisition
decisions. The interest rate was not shown in Figure 3; here it is clear that the interest rate is
formulated in the banking sector and that the interest rate affects both consumption and
production submodel decisions.
Main Model Equations
Left Side of Equation
1
GDP
2
labor & capital
3
productivity
of labor & capital
4
aggregate demand
Right Side of Equation
labor & capital * productivity of labor & capital
factors of production
units
$/year
FP
multifactor productivity
$/yr/FP
nominal aggregate demand / price index
$/year
MacroLab: The Model 26
5
nominal aggregate demand
6
price index
7
inventories(t)
consumption + investment + govt purchases+ US export
receipts - US import pmts
Price
inventories(t - dt) + (GDP - aggregate demand) * dt
$/year
1/1
$
INIT = desired inventories *
(init(GDP) / init(aggregate demand))
8
wages & dividends
9
taxes
10
business saving
11
Firms $ (t)
nominal disposal income
$/year
nominal taxes
$/year
nominal business saving
$/year
Firms $(t - dt) + (govt purchases + investment + cash chgs +
consumption + US export receipts - business saving - taxes wages & dividends - US import pmts) * dt
$
INIT = (consumption + investment +govt purchases + US
export receipts - US import pmts)/12
12
Homes $ (t)
Homes $(t - dt) + (wages & dividends + transfer pmts consumption - personal saving) * dt
$
INIT = (transfer pmts + wages & dividends) / 12
13
Govts $ (t)
Govts $ (t - dt) + (taxes - govt purchases - govt saving transfer pmts) * dt
$
INIT = taxes / 12
14
Savings(t)
Savings(t - dt) + (business saving + net domestic deposits +
govt saving + personal saving + saving by RW in US investment) * dt
$
INIT = initial M2 - Firms - Govts - Homes
15
transfer pmts
nominal transfer payments
$/year
16
consumption
nominal consumption
$/year
17
personal saving
nominal personal saving
$/year
18
investment
nominal investment
$/year
19
govt purchases
nominal govt purchases
$/year
20
govt saving
- government deficit
$/year
21
US export receipts
H: smth3(historical nom exports,5)
$/year
E: nominal US receipts for exports $
22
US import pmts
H: smth3(historical nom imports,5)
$/year
E: nominal US pmts for imports $
23
saving by RW in US
H: smth3(historic net capital inflow,5)
$/year
E: US net capital inflow $
24
net domestic deposits
25
cash chgs
net domestic deposit chg
$/year
cash withdrawals
$/year
MacroLab: The Model 27
factors of production
multifactor productivity
Price
desired inventories
nominal disposal income
nominal taxes
nominal business saving
initial M2
nominal transfer payments
nominal consumption
nominal personal saving
nominal investment
nominal govt purchases
government deficit
historical nom exports
nominal US receipts for exports $
historical nom imports
nominal US pmts for imports $
historic net capital inflow
US net capital inflow $
net domestic deposit chg
cash withdrawals
Productivity Submodel
Productivity Submodel
Price Submodel
Labor Submodel
Income Distribution Submodel
Income Distribution Submodel
Income Distribution Submodel
Data Sector
Government Submodel
Consumption Submodel
Consumption Submodel
Capital Submodel
Government Submodel
Government Submodel
Data Sector
Exchange Rate Submodel
Data Sector
Exchange Rate Submodel
Data Sector
Exchange Rate Submodel
Banking Submodel
Banking Submodel
Figure 20. Main Model Equations
MacroLab: The Model 28
5.2 Labor Sector within the Production Submodel
Labor’s Location within the Main Model
Labor Sector within the Production Submodel
Figure 21
The labor sector stock-and-flow structure is displayed in Figure 21, and Figure 22
contains a corresponding
feedback loop diagram.
Textbooks emphasize that the
level of employment depends
on both the supply and demand
for labor (Mankiw ch. 10;
McConnell/Brue, ch. 8). In
the labor sector, the demand
for labor is called “desired
labor,” and it depends
positively on expected demand
for goods and services and
negatively on average wages—
total wages divided by
Figure 22. Feedback Loop Structure of the Labor Sector
Employment.
MacroLab: The Model 29
Labor Sector Equations within the Production Submodel
Left Side of Equation
26
Right Side of Equation
Employment(t - dt) + (net hiring) * dt
units
persons
Employment(t)
INIT historical = historic employment
INIT experimental = 100
27
net hiring
28
desired labor
29
net hiring adj time
30
nominal expected demand
31
nominal wages(t)
if(Labor Force>Employment)then(((desired laborEmployment)/net hiring adj time))else(0)
persons
/year
(nominal expected demand*labor's income share) /
(nominal wages / Employment)
persons
.5
years
price index * real expected demand
$/year
nominal wages(t - dt)+(net chg in wages)*dt
$/year
INIT = indicated nomimal wages
32
net chg in wages
(indicated nomimal wages-nominal wages)/wage pmt period
$/yr/yr
33
wage pmt period
.08
years
34
indicated nominal wages
GDP*labor's income share*smth1(price index, time to adjust
wages for prices)*smth1(unemployment effect on wages,
time to adjust wages for UR)
$/year
35
time to adjust wages for
prices
1
years
36
time to adjust wages for UR
.25
years
37
UR effect on wages
GRAPH(unemployment rate/natural UR)
1/1
(0.00, 1.50), (0.2, 1.25), (0.4, 1.14), (0.6, 1.08), (0.8, 1.04),
(1.00, 1.00), (1.20, 0.97), (1.40, 0.935), (1.60, 0.92), (1.80,
0.91), (2.00, 0.9)
38
unemployment rate
39
natural UR
40
UR effect on LF
100 * (1 - (Employment / Labor Force))
1/1
5
1/1
UR effect on LF = GRAPH(unemployment rate/natural UR)
1/1
(0.00, 1.005), (0.2, 1.004), (0.4, 1.003), (0.6, 1.002), (0.8,
1.001), (1.00, 1.00), (1.20, 0.999), (1.40, 0.998), (1.60,
0.997), (1.80, 0.996), (2.00, 0.995)
41
Labor Force(t - dt) + (joining labor force) * dt
Labor Force(t)
persons
INIT historical = Employment / (1-(historic employment /
100))INIT experimental = Employment / ((1-initial
unemployment rate / 100))
42
joining labor force
(net chg in wrk age pop*labor force joining rate)+(if(working
age population>Labor Force)then((UR effect on LF*Labor
Force-Labor Force)/labor force adj time)else(0))
persons
/year
43
labor force joining rate
.70
1/1
44
labor force adj time
.5
years
MacroLab: The Model 30
45
working age population(t)
working age population(t - dt) + (net chg in wrk age pop) * dt
persons
INIT historical = historic working age population
INIT experimental = Labor Force /.65
46
net chg in wrk age pop
working age population*smth3(working age pop net growth
fraction,5)
47
real expected demand
smth1(aggregate demand,demand perceptions adj
time,aggregate demand-inventory adjustment)+inventory
adjustment
$/year
48
demand perceptions adj
time
.5
years
49
inventory adjustment
(desired inventories-inventories) / inventory adj time
$/year
50
inventory adj time
.5
years
51
desired inventories
desired inventory coverage * aggregate demand
historic employment
labor's income share
GDP
price index
initial unemployment rate
historic working age population
working age pop net growth fraction
aggregate demand
inventories
desired inventory coverage
persons
/year
$
Calculations Sector
Productivity Sector of the Production Submodel
Main Model
Price Sector of the Production Submodel
Calculations Sector
Calculations Sector
Calculations Sector
Main Model
Main Model
Data Sector
Figure 23. Labor Sector Equations
More precisely, desired labor (#28 in the equations table) depends on the nominal
expected demand (#30) and nominal wages (#31). Above-average profit opportunities exist
when product prices are rising faster than the price of labor. An increase in the perceived
demand for goods and services causes an increase in the demand for the labor required to
produce those goods and services, ceteris paribus. Nominal expected demand depends on
real expected demand (#48) and the price level. Real expected demand is a smoothed
function of aggregate demand plus an adjustment for inventories (#50). The time for
producers to adjust their perceptions of demand (#49) is estimated to be .5 years, as is the
average inventory adjustment time (#51).2
An increase in the average nominal wage reduces the demand for labor, ceteris paribus.
In equilibrium, total wages are defined as labor’s normal share of national income (equal to
GDP in equilibrium). Labor’s income share is assumed to be .75.3 Disequilibrium conditions
—reflected in changing levels of prices and unemployment—will push wages above or below
the norm. Indicated nominal wages (#34) is, therefore, a function of GDP, labor’s share of
income, the price index, and the unemployment rate. Wages are assumed to be paid monthly
(#33).
The unemployment rate (#38) reflects both the supply (labor force, #39) and demand
(employment, #26) for labor. A rise in unemployment puts downward pressure on starting
2
Unless indicated otherwise, all delay structures are modeled as first-order delays. N. Forrester (1982) used .5
and .4 years for the perceived demand and inventory adjustment time constants, respectively.
3
N. Forrester (1982) made the same assumption, based on national income accounts data.
MacroLab: The Model 31
wages, thus keeping total and average wages lower than they would be otherwise. The
nonlinear function describing the negative effect of unemployment on wages (#37) is based
on Blanchflower and Oswald (1994), who suggest a wage elasticity of unemployment equal
to about - 1/10. The effect is not immediate, however, and the average adjustment time (#36)
is assumed to be .25 years.
In Figure 22, loop C1 is a counteracting feedback loop connecting employment, the
unemployment rate, nominal wages, and desired labor. Assume desired labor increased
suddenly, due to an increase in aggregate demand. That would set in motion a hiring process
that would eventually raise employment and lower the unemployment rate. Gradually, rising
wages would constrain the growth in desired labor and employment, and that would put
upward pressure on the unemployment rate, even if there had been no changes in the labor
force (defined as those persons with a job or seeking a job).
It is likely, however, that another counteracting loop—C3—would have been expanding
the labor force ever so slightly. When the unemployment rate fell initially (and wages rose),
the employment outlook would have improved and the opportunity cost of remaining
unemployed would have risen. That would have caused a few more working-age adults to
join the job search, and the rise in the number of people seeking jobs would have put upward
pressure on the unemployment rate. Thus, the initial drop in unemployment would set in
motion forces that would eventually constrain the demand for labor and—at the same time—
boost the labor supply. Unemployment would not keep falling.
Prices also influence wages. Changes in workers’ cost-of-living will eventually affect
average periodic wage adjustments—assumed here to occur annually (#35). The submodel
behavior demonstration at the end of this subsection focuses on the effects of a change in
prices.
Input Response Tests. To confirm that the labor sector submodel does perform as expected
—a validation procedure Ford (1999) calls verification—a series of input response tests was
conducted. Step or pulse shocks were administered to five exogenous inputs. Based on the
links from the parameters to the unemployment rate in the feedback diagram in Figure 22
above, the unemployment rate should rise, ceteris paribus, when permanent increases occur
in GDP or inventories, since the former raises the cost of labor and the latter lowers the
demand for labor. The unemployment rate should decline when aggregate demand increases
because demand for labor permanently increases. When prices increase, the unemployment
could rise or fall—or both—depending on the timing of wages increases. The step increase
in the working-age population (and, therefore, the labor force) should push the
unemployment rate up immediately, but that will put extreme downward pressure on starting
wages, which will bring the unemployment rate down to lower levels almost as sharply.
After that, the unemployment rate should return to its initial value if wages adjust fully to the
changing labor market.
When interpreting these hypotheses and the simulation results in Figure 24 below, it is
necessary to keep in mind that, while all five inputs are exogenous in the labor sector, only
the working-age population is exogenous in the full model. Thus, in four cases, the behavior
in the labor sector will not necessarily be the same as would occur when the full model is
MacroLab: The Model 32
running. Within the labor sector, for example, when the inventory shock is ON and a
permanent 1 percent increase in the inventory occurs, the unemployment rate rises
permanently. If such an inventory shock occurred in the full model, the reduction in
employment would reduce production and inventories would go back down to normal levels.
As that occurred, the unemployment rate would also go back down to its "natural" rate.
Nevertheless, these input shock tests in the submodel are useful for confirming that what
should happen within this sector does happen (e.g., an increase in inventories should raise the
unemployment rate). The results of the input shock tests are displayed in Figure 24, and each
behavior is consistent with the expected behavior. (The tendency for oscillations to occur is
discussed later in this subsection.)
A: Shocks to Population, GDP, and Price
B: Shocks to Aggregate Demand & Inventories
Figure 24. Unemployment Rate Response to Exogenous Input Shocks in Labor Sector
Parameter Sensitivity Analysis. The labor sector contains two graph functions (#38
and #41) and eight time constants: net hiring adjustment time (#30), wage payment period
(#34), time to adjust wages for prices (#36), time to adjust wages for the unemployment rate
(#37), labor force joining rate (#43), labor force adjustment time (#44), demand perceptions
adjustment time (#48), and inventory adjustment time (#50). Thirty sensitivity tests were
conducted—three for each parameter at values equal to, below, or above the parameter’s
default value in the model—and the behavior of the unemployment rate was examined when
there was an exogenous shock to the model. The particular adjustments selected for each
parameter test depended on the range of uncertainty in the default estimate. For example, the
net hiring adjustment time—assumed to be .5 years—was adjusted down to .25 years and up
to 1 year. Three simulations were also run for each graph function, with the slopes varied
above and below the default assumptions. For example, the slope of the unemployment rate
effect on wages was varied from -.05 to -.10 (default assumption) to -.15, based on the ranges
reported in Blanchflower and Oswald (1994).
Based on the individual tests, the labor sector model was most sensitive to variations in
the net hiring adjustment time, the time to adjust wages to changes in the unemployment rate,
and the elasticity of wages with respect to the unemployment rate. In future refinements of
MacroLab, reducing the uncertainty in estimates of these parameters will be a priority
research task. The model’s relative lack of sensitivity to the demand perception adjustment
time and the inventory adjustment time could be misleading, however, since aggregate
demand and inventories received no feedback effects within the labor sector in these
sensitivity tests.
MacroLab: The Model 33
Extreme Conditions Tests. An additional validation test involves subjecting the model
to extreme conditions and judging the realism of its response. In the labor sector, a serious
error to avoid is hiring people who do not exist. Therefore, the net hiring rate (#28) can be
greater than zero only when the labor force is greater than employment. In a similar fashion,
the inflow (#43) to the labor force stock can be greater than zero only when the number of
working-age adults is greater than the size of the labor force.
Illustration of Labor Sector Behavior. The input shock tests above revealed strong
oscillatory behavior in the labor sector, which we now examine by subjecting the labor sector
to another exogenous one percent price increase. Given the structural relationships described
above, producers would initially respond to the nominal increase in product demand by hiring
more labor. Eventually, the general rise in prices would translate into wage adjustments.
Meanwhile, the rise in employment would lower the unemployment rate, and the relative
scarcity of labor would also gradually increase pressure to raise wages. For purposes of this
experiment, average delay times were set at one year (“slow”), one week (“quick”), or a
combination of slow and quick.
A: When Wages Adjust Slowly to Both
Prices and the Unemployment Rate
B: When Wages Adjust Quickly to Prices
but Slowly to the Unemployment Rate
C: When Wages Adjust Slowly to Prices
but Quickly to the Unemployment Rate
D: When Wages Adjust Quickly to Both
Prices and the Unemployment Rate
Figure 25. Price Shock Experiment with the Labor Sector Model
Four scenarios were simulated, with the various combinations of slow and quick wage
responses to changes in the price index and the unemployment rate. The results are displayed
graphically in panels A-D of Figure 25. (The vertical axis scales in Figure 25 are such that
the changes in price, wages, and employment are comparable in percentage terms. The scale
for the unemployment rate is necessarily larger.) With varying delays in each scenario, the
MacroLab: The Model 34
step-up in price was followed—and eventually matched in percentage terms—by wages.
Employment and the unemployment rate naturally moved in opposite directions but
eventually stabilized at their initial levels. Ultimately, therefore, the same number of people
were working and their average real wage was unchanged. That is usually the point—and the
end—of the textbook version of the story. The transition patterns were quite different in each
scenario, however, and analyzing the differences in this simulation experiment can shed light
on the origin of the dynamics.
When the wage response was slow to both price and unemployment rate changes (panel
A), strong fluctuating patterns emerged and instability continued for more than four years.
When the wage response was quick to both price and unemployment (panel D), the submodel
system stabilized in six months. In panel B, a quick wage response to price, even when
responding slowly to unemployment, reduced the amplitude of the fluctuations, but the
oscillatory tendency remained. In panel C, a quick wage response to unemployment (coupled
with a slow response to prices) eliminated the fluctuations, but more than two years passed
before the system regained equilibrium.
The source of the interesting dynamics in this example is found in the counteracting
feedback loop C1 in Figure 26 (where each pair of vertical bars indicates a location of
significant delays along the loop). With two stocks—the material stock employment and the
information stock nominal wages—in the counteracting loop, there exists the necessary
condition for oscillations. Sufficiency is provided by the significant delays that affect
changes in nominal wages (Sterman 2000). When those delays are virtually eliminated in
panel D, the fluctuations disappear. This example illustrates the behavior of the labor sector,
and it also demonstrates a method for isolating the structure responsible for that behavior.
Figure 26. Oscillations Result from Delays in the
Counteracting Feedback Loop C1
MacroLab: The Model 35
5.3 Capital Sector within the Production Submodel
Figures 27-29 provide four perspectives of the capital sector. The top panel of Figure
27 is a reminder of capital’s position within the main model, while the bottom panel provides
a detailed view of its stock-and-flow structure inside the production submodel. The equations
underlying that structure are listed in Figure 28 and, finally, a feedback loop diagram in
Figure 29 highlights key relationships.
Capital’s Location within the Main Model
Capital Sector within the Production Submodel
Figure 27
MacroLab: The Model 36
Capital Sector Equations within the Production Submodel
Left Side of Equation
52
nominal investment
53
Capital(t)
Right Side of Equation
capital additions * price index
Capital(t - dt) + (capital additions - capital depreciation) * dt
units
$/year
$
INIT historical = private fixed assets
INIT experimental=(capital's income share*initial
production) / ((initial interest rate/100)+1/(avg life of capital))
54
capital additions
capital on order / capital delivery time
$/year
55
capital depreciation
Capital / avg life of capital
$/year
56
avg life of capital
14
years
57
capital delivery time
1.5
years
58
capital on order(t)
capital on order(t - dt)+(capital orders - capital additions)* dt
$
INIT = capital delivery time * desired capital orders
59
capital orders
desired capital orders
$/year
60
desired capital orders
capital depreciation + (( desired capital -Capital) / capital
adj time)
$/year
61
capital adj time
3
years
62
desired capital
long run expected output*desired capital output ratio
63
desired capital output ratio
64
expected labor cost
productivity ratio
65
expected cost of capital
(smth1(interest rate,capital cost perceptions adj time)/100)
+(1/avg life of capital)
1/year
66
capital cost perceptions
adj time
3
years
67
long run expected output(t)
long run expected output(t - dt) + (chg in long run expected
output) * dt
$/year
reference capital output ratio
*expected labor cost productivity ratio
/(expected cost of capital/init(expected cost of capital))
smth3((avg real wage/init(avg real wage))
/(output per worker/init(output per worker)),1)
$
years
1/1
INIT = GDP
68
chg in long run
expected output
69
expected output adj time
price index
private fixed assets
capital's income share
initial production
initial interest rate
interest rate
GDP
aggregate demand
reference capital output ratio
avg real wage
output per worker
(aggregate demand-long run expected output)/expected
output adj time
3
Price Sector of Production Submodel
Data Sector
Productivity Sector of Production Submodel
Data Sector
Interest Rate Sector of Banking Submodel
Interest Rate Sector of Banking Submodel
Main Model
Main Model
Data Sector
Data Sector
Data Sector
Figure 28. Capital Sector Equations
$/year/
yr
years
MacroLab: The Model 37
Textbooks emphasize
that the rate of investment in
capital equipment and
structures is a function of the
expected financial return on
such investments. When the
revenue expectations rise or
capital cost expectations fall
—or some combination
thereof resulting in higher
expected profits—
investments will be made
(Mankiw, ch. 8 and
McConnell/Brue, ch. 9). As
the diagrams in Figures 27
and 29 illustrate, and the
Figure 29. Feedback Loop Structure of the Capital Sector
equations in Figure 28
specify, the investment
decisions within the capital sector of MacroLab reflect those same considerations.
Business spending on capital equipment and structures is presumed to occur as capital
orders are transformed into real additions to the capital stock. Certainly, some advance
payments may accompany orders but, for modeling purposes, the assumption was made that
the payment schedule would roughly correlate with actual deliveries. The role of
“investment” in these diagrams, therefore, may puzzle readers who think in terms of
investment “causing” capital to be added; they may have expected the causal link arrow to
point from investment to capital additions. The motivation for the current formulation is the
conceptualization of investment as the outcome of a capital decision-making process that
generates “orders” for capital, along with a plan to pay for those orders. The investment
intention certainly precedes the orders, but the investment spending is assumed to coincide
with fulfillment of the plan. No claim is made that this is the best way to formulate the
relationship between capital decision-making and actual spending for new equipment and
structures. However, it does facilitate the integration of the real and nominal sides of the
MacroLab economy, and it does so while maintaining consistency with the consensus
textbook explanation of the capital acquisition process.
To describe the steps in that process within the capital sector of MacroLab, the feedback
loop diagram (Figure 29) will be used, but references to variables will include equation
numbers from the table (Figure 28). As noted above, nominal investment (#52) is the
nominal payment for the real capital additions (#54), which result from capital orders (#59).
Desired capital orders (#60) flow from a decision rule that starts with capital depreciation
(#55) and then adds the difference between desired capital (#62) and current capital (#53).
Desired capital rises when long run expected output (#67) rises, following an extended period
(#69) of reviewing trends and updating perceptions of aggregate demand trends.
On the cost side, there is assumed to be a “normal” expectation of the capital
requirements to support a planned rate of output within every industry. That figure is
MacroLab: The Model 38
aggregated here and called the “reference” capital-output ratio. Historically, that ratio has
been about 2/1 in the US, meaning that a $10 trillion economy—in GDP terms—would
depend on a capital stock worth about $20 trillion. When a simulation begins, an initial
reference capital-output ratio is calculated, based on the initial value of the capital stock and
the initial production rate (GDP). (The same initial equation is used in historic mode, but the
reference ratio is based on historical data.)
The reference capital-output ratio is adjusted to a “desired” ratio (#63). There would be
an upward adjustment when capital costs were expected to be relatively low, and a downward
adjustment when expected to be relatively high. In equilibrium, the desired and reference
capital-output ratios would be equal. The cost adjustment has two components: the expected
cost of capital (#65) and the expected labor cost-productivity ratio (#64). When interest rates
rise and/or the average life of capital (#56) declines, the cost of capital rises and a lower
capital-output ratio is desired. When real wages rise faster than output per worker, relatively
less labor is desired, and a higher capital-output ratio is desired. These impacts on the desired
capital-output ratio are formulated as linear relationships in the current version of the model;
nonlinear effects are probably more likely.
Parameter Sensitivity Analysis. The capital sector contains six time-related parameter
assumptions: average life of capital (#56), capital adjustment time (#61), capital delivery time
(#57), time to smooth labor cost productivity ratio (in #64), capital cost perception time
(#66), and expected output adjustment time (#69). Estimates for average life of capital (14
years) and expected output adjustment time (3 years) are based on N. Forrester (1982). The
source for estimates of capital adjustment time (3 years) and capital delivery time (1.5 years)
is Sterman (2000). The time to smooth the labor-cost productivity ratio (1 year) is based on
the assumption of annual reviews of costs and productivity. The capital cost perception time
(3 years) is based on the assumption that the delay in responding to changes in interest rates
would be about the same as the delayed response to changes in demand. Following the
procedure outlined in the labor sector subsection, each parameter was tested separately to
determine the capital sector’s sensitivity to variations. Then, the more critical parameters
were tested in combinations. Variations in three parameters had significant implications for
the behavior of the capital sector: average life of capital, capital adjustment time, and capital
delivery time.
In experimental mode (which is used in testing the submodel), the initial value of the
capital stock depends, in part, on the average life of capital. Thus, a change in the
assumption for the average life of capital affects more than just the model’s response to the
demand shock; it also affects the initial investment necessary to maintain the initial
equilibrium condition. Thus, the starting point changes—a longer life of capital means less
initial investment is needed to replace discards. Therefore, when the sensitivity tests reveal
vastly different investment rates, given variations in the average life of capital, that is
somewhat misleading as an indicator of model sensitivity. A good estimate for average life of
capital is important, however, because of its impact on the user cost of capital. When running
in historic mode with a consensus empirical estimate of the capital stock, one way to gauge
the accuracy of the average life of capital assumption is to compare the initial simulated
investment rate with the initial historical investment rate, under the assumption that actual
historical investment rates would be close to desired historical rates.
MacroLab: The Model 39
Also important for the characteristic performance of the capital sector model were the
assumptions about capital adjustment time and capital delivery time. Investment showed
signs of oscillation when the capital adjustment time was reduced. When delivery times
lengthened, investment diverged from its trend for a much longer time. These two time
constants were particularly worth investigating because they influence a major counteracting
feedback loop. Loop C in Figure 29 links desired capital orders (#60), capital orders, capital
on order (#58), capital additions, and capital. Sterman (2000) provides an in-depth
discussion of the oscillatory tendencies in the capital adjustment process when capital
adjustment time (the speed at which producers attempt to close capital gaps) is too short,
relative to the delivery time (the speed with which capital can actually be installed). A
combination sensitivity test was conducted, and the model was shocked with a 10 percent
demand increase. In Figure 30, the blue investment curve reflects a situation in which the
capital adjustment time (1.5 years) is actually shorter than the delivery time (2.25 years), and
the oscillatory tendency is evident. The red curve reflects the combination of default
assumptions in MacroLab.
Figure 30. Investment Sensitivity To Time Constants
(shock: 10% increase in demand)
Illustration of Capital Sector Behavior. Figure 31 displays the response of investment
and capital when interest rates drop from 5 to 4 percent—a 20 percent decline. There is a
gradual rise in desired capital (red), due to the delay in updating capital cost expectations. As
desired capital is translated into orders, investment (black) rises and additional capital (blue)
begins to accumulate. As the capital gap closes, investment decreases from its peak but
stabilizes at a new higher rate, reflective of the new higher rate of depreciation associated
with the larger stock of capital.
Figure 31. Capital Sector Submodel Behavior
(shock: 20% decrease in interest rates, from 5% to 4%)
MacroLab: The Model 40
5.4 Productivity Sector within the Production Submodel
At the beginning of this chapter, the first Mankiw principle concerned the concepts of
productivity and factors of production. In this brief subsection, MacroLab’s formulation of
those concepts is presented. Figure 32 provides both an overview and a detailed view of the
productivity sector within the production submodel. In the top panel, “productivity of labor
& capital” at the main model level equals “multifactor productivity” at the sector level.
Likewise, “labor & capital” in the main model equals “factors of production” inside the
productivity sector. GDP is the product of the two.
GDP
=
=
=
=
productivity of labor & capital * labor & capital
multifactor productivity * factors of production
(($ trillion/year) / FP ) * FP
$ trillion/year
Location of Productivity in the Main Model
Productivity Sector within the Production Submodel
Figure 32
MacroLab: The Model 41
Productivity Sector Equations within the Production Submodel
Left Side of Equation
70
Right Side of Equation
multifactor productivity(t - dt) + (chg in productivity) * dt
multifactor productivity(t)
71
chg in productivity
72
labor's income share
73
Units
$/yr/FP
INIT = initial GDP / ((capital^capital's income share)*
(effective labor^labor's income share))
multifactor productivity*(multifactor productivity growth rate
%/100)
($/yr/FP)
/year
.75
1/1
capital's income share
1-labor's income share
1/1
74
multifactor productivity
growth rate %
H: smoothed historic productivity growth rate
E: 0
75
factors of production
76
effective labor
77
1/year
(Capital^capital's income share) *
(effective labor^labor's income share)
overtime index*Employment
FP
persons
overtime index(t - dt) + (OT index chgs) * dt
1/1
overtime index(t)
INIT = 1
78
OT index chgs
79
indicated overtime index
80
OT adj time
initial GDP
capital
Employment
real expected demand
GDP
(indicated overtime index - overtime index) / OT adj time
1/year
real expected demand / GDP
.25
1/1
years
Calculations Sector
Capital Submodel
Labor Submodel
Labor Submodel
Main Model
Figure 33. Productivity Sector Equations
The Cobb-Douglas production function is formulated as follows:
K
= capital
MPK = marginal productivity of capital
L
= labor
MPL = marginal productivity of labor
A
= multifactor productivity
then
GDP = A * (K^MPK) * (L^MPL)
If the model is running in experimental mode, GDP is $10 trillion/year initially. In
historic model, GDP is the actual historical value for the year beginning the simulation.
Thus, initially, multifactor productivity (#71 in the equation list) is:
A
= initial GDP / ((K^MPK) * (L^MPL))
and the initial value for the factors of production (#75) is (K^MPK) * (L^MPL).
MacroLab: The Model 42
Using the standard textbook assumption of constant returns to scale, the relative
productivities of labor and capital sum to one. The standard method of imputing those
productivities is to use historical data on the national income shares going to labor (#72) and
capital (#73), under the assumption that shares of real income correspond to relative
contributions to multifactor productivity. Accordingly, labor’s contribution is assumed to
be .75, with capital’s contribution being .25.
In experimental mode, it is useful to initialize the model in equilibrium and, in that case,
the growth rate of productivity is set to zero. The interface controls permit assigning a nonzero growth rate, however, whether in experimental or historic mode. In historic mode, the
choice of growth rate depends on the time period under study and the purpose of the
simulation exercise. If the purpose is to track historical trends, the average growth rate is
used for periods sharing approximately the same rate. If the purpose is to forecast, as in the
five-year forecast exercise in section 4, the smoothed average growth rate for the five years
preceding each forecast was used, so that the model would use only information that would
have been available in real time.
The “overtime index” (#77) could have been placed in the labor sector. However, it
was placed in the productivity sector because it relates to the issue of management of the
labor stock during the early periods of recession and expansion—an issue that manifests itself
in productivity data during those periods. The conventional wisdom and frequent textbook
explanation is that the first reaction to a demand decline is not layoffs but work slowdowns,
or “undertime.” Labor is reassigned to nonproductive activities, and measured output per
worker declines. If the situation deteriorates further, layoffs occur and employment actually
declines. When signs of recovery appear, the first reaction is to use “overtime” rather than
immediately hire new workers (or call back laid-off workers), which results in an increase in
measured labor productivity. Employment eventually increases when overtime costs become
excessive, at which point producers conclude that the recovery is really underway.
The overtime index, therefore, adjusts employment and creates a variable called
“effective labor” (#76), which is used in the production function. When aggregate demand is
less than GDP, the overtime index is less than one, and effective labor is less than
employment. When demand exceeds production, the overtime index is greater than one, and
effective labor is greater than
one.
In equilibrium, the
overtime index equals one, and
e ff e c t i v e l a b o r e q u a l s
employment. Producers are
assumed to adjust overtime
more quickly than they adjust
the actual labor stock, and the
average adjustment time is
assumed to be .25 years (#80).
Figure 34 illustrates the
overtime index in action. The
behavior in the graph was
Figure 34 Productivity Submodel Test
triggered by a ten percent step
MacroLab: The Model 43
reduction in demand—simulating the onset of a recession. While employment remains
constant, effective labor falls as some workers are re-assigned to nonproductive tasks.
Output per worker = (multifactor productivity*factors of production)/employment; thus,
output per worker falls since “factors of production” declines when effective labor declines.
Again, it is important to remember that the exogenous inputs to this sector are
endogenous when the full model is running. Thus, for a given shock, the behavior in the
productivity sector will not be the same as would occur when the full model is running. For
example, when the demand shock is ON and a permanent 10 percent decrease occurs, labor
productivity (output per worker) falls permanently. If such a demand shock occurred in the
full model, the reduction in demand would eventually reduce employment and output per
worker would rise since nothing has changed the skill level of the workers or the technology
in the production process.
The most important validation test in this sector is to subject the submodel to extreme
conditions relating to the factors of production. The Cobb-Douglas production function
requires both labor and capital to interact. If labor had no tools (i.e., capital = 0), there should
be no production. If tools lay idle because there were no workers (i.e., employment = 0),
there should be no production. This test was implemented with a pulse outflow function in
each of the two factor stocks. In year 1, all capital was drained from the stock, and the
factors of production immediately dropped to zero, as expected. The same result was
achieved with the employment stock.
MacroLab: The Model 44
5.5 Price Sector within the Production Submodel
The “price index” at the main model level (top panel of Figure 35) is equal to the
information stock “price” within the price sector of the production submodel (bottom panel).
As both theory and textbooks (Mankiw, ch. 4; McConnell/Brue, ch. 3) would recommend,
price in the model is determined by demand and (the cost of) supply. The “cost effect on
price” is a weighted average of the domestic and import unit costs. The “demand effect on
price” is equal to 1.00 when GDP and real expected demand are equal, but is greater (less)
than 1.00 when expected demand is greater (less) than GDP. The average adjustment time for
price is estimated at .25 years, based on Blinder (1997).
Location of Price in the Main Model
Price Sector within the Production Submodel
Figure 35
MacroLab: The Model 45
Price Sector Equations within the Production Submodel
Left Side of Equation
81
Right Side of Equation
Price(t - dt) + (net price chgs) * dt
units
1/1
Price(t)
INIT = 1.00
82
net price chgs
(indicated price - Price) / price adj time
1/year
83
price adj time
.25
years
84
indicated price
init(Price)*cost effect on price * demand effect on price
1/1
85
cost effect on price
(wt of import costs in US*unit import costs US $)+((1-wt of
import costs in US)*unit production costs US $)
1/1
86
unit production costs US $
labor's income share*((nominal wages/GDP)/(init(nominal
wages)/init(GDP)))
+(1-labor's income share)*((nominal wages/GDP)/(init
(nominal wages)/init(GDP))) *(smth1(user cost of capital,5)/
init(user cost of capital))
1/1
87
wt of import volume in US
1 - ( GDP / ( GDP + real imports into US))
1/1
88
demand effect on price
real expected demand / GDP
1/1
nominal wages
unit import costs US $
GDP
real imports into US
real expected demand
labor’s share of income
user cost of capital
Labor Sector of Production Submodel
Exchange Rate Submodel
Main Model
Exchange Rate Submodel
Labor Sector of Production Submodel
Productivity Sector of Production Submodel
Capital Sector of Production Submodel
Figure 36. Price Sector Equations
Domestic unit production costs are roughly weighted according to labor costs and
capital costs. In principle, capital costs should reflect a weighted average of the cost for each
unit of capital in use, which could be formulated as a co-flow similar to the determination of
average interest cost for servicing debt in the government submodel. However, an additional
complex equation structure for that purpose seemed unwarranted, given that most of the
production costs are due to labor.
Unit production costs (#86) in the equation list is an attempt to give some appropriate
weight to capital costs in a simplified fashion. The relative change in capital costs is
computed with the current “user cost of capital” divided by its initial value at the beginning
of the simulation and then smoothed over five years so that changes in current interest rates
do not radically alter the estimate of accumulated interest charges that span several years.
The relative change in capital cost is then added to the relative change in unit labor
production costs, with each weighted according to shares of income (i.e., shares of costs).
To illustrate, assume that over the course of a simulation, unit labor costs rose 30
percent and interest rates rose by an amount that caused user cost of capital to rise by 10
percent when calculated after smoothing. The domestic unit production costs would then be
calculated by (.75*1.30 + .25*1.10), which would be 1.25—a weighted average increase of
25 percent. A simulation run using these assumptions in the price sector submodel and
MacroLab: The Model 46
generating the same
displayed in Figure 37.
result
is
Figure 38 illustrates the
weighting process involving import
costs.
The foreign sector is
activated, and for one year the
weight of imports (black curve) is 10
percent of the total domestic and
import volume.
The initial unit
import cost is the same as initial US
production costs, both equal to 1.00.
For the first six months, therefore,
US prices (blue) do not change.
Figure 37. Price Submodel Test of
Weighting Labor and Capital Costs
The green curve shows the domestic demand price effect when a 5 percent increase in
aggregate demand occurs at the six-month point, followed by rising prices (blue curve). If
nothing else happened, prices would rise 5 percent (since there is no feedback effect on either
demand or wages within the price sector). At the one-year point, however, an exogenous 20
percent increase in imports occurs,
which raises the import weight to 12
percent (holding GDP constant in
this sector). In addition, the average
price of all imports (red curve) rises
exogenously by 25 percent, which
bumps the blue price curve to a
higher trajectory. At the end of the
simulation, the price level has risen
by 8 percent—5 percent due to
domestic demand growth and 3
Figure 38. Price Submodel Test
percent because 12 percent of the
of Weighting Domestic and Import Costs
total volume costs 25 percent more.
Price Adjustment Delay. Variation in the price adjustment time (#83 in the equation
list) has a significant effect on the behavior of the submodel—in the obvious way of
shortening or lengthening the phase-in of price changes. Moreover, when the full model is
running, price plays a key role in several feedback loops, and variations in price adjustment
time have both amplification and oscillatory impacts on the behavior of the full model. The
source for the .25 year adjustment period assumption is Blinder‘s (1997) survey of 186
companies that represented about 85 percent of the private, non-farm GDP. The survey led
Blinder to conclude that “the typical lag of a price change behind a shock to either demand or
cost is about three months.”
MacroLab: The Model 47
5.6 Income Distribution Submodel
The submodel for distributing national income is very simple. Income originates on the
real side of the economy—where production occurs. Adjusted to current dollars by the price
index, it is distributed in three directions. After taxes (but before transfer payments), about
two-thirds goes to households (called “Homes” in the main model). Governments get about
one-fourth by taxing individuals and businesses. After paying wages, dividends and taxes,
businesses retains less than one-tenth of national income for reinvestment in capital
equipment and structures. Figure 39 displays an overview and a detailed structure. The
equations are in Figure 40.
Location of Income Distribution Submodel within the Main Model
Income Distribution Submodel
Figure 39
MacroLab: The Model 48
Income Distribution Submodel Equations
Left Side of Equation
Right Side of Equation
units
89
nominal wages & dividends
90
nominal dividends
91
dividends pct
.55
92
nominal taxes
personal taxes+business taxes
$/year
93
personal taxes
(nominal wages + nominal dividends) * personal tax pct
$/year
94
business taxes
max(0,(business tax pct) * operating surplus)
$/year
95
operating surplus
nominal sales - nominal wages
$/year
96
disposable business income
operating surplus - business taxes
$/year
97
nominal business saving
disposable business income - nominal dividends
$/year
nominal wages
personal tax pct
business tax pct
price index
GDP
nominal wages + nominal dividends - personal taxes
$/year
smth1(disposable business income * dividends pct,.25)
$/year
1/1
Labor Submodel
Calculations Sector
Calculations Sector
Price Sector of Production Submodel
Main Model
Figure 40. Income Distribution Submodel Equations
Several simplifying assumptions were made with regard to taxes. There is a single
personal tax rate and a single business tax rate. The tax base for business is assumed to be
the operating surplus (#95); thus, no taxes are levied on production or sales. Even if the total
business tax revenue (#94) is approximately correct, the tax structure in the model does not
capture tax incentive effects that arise from different types of taxes levied at different points
in the economy. Another simplifying assumption is that the personal tax rate is the same for
wages and dividends (#89). A mildly progressive aggregate tax structure is achieved by
making the personal tax rate vary inversely with the unemployment rate, a correlation
observable in the US economy.
The functionality of this submodel is easily imagined, but Figure 41 provides an
illustration. The shock in this case
is a 30 percent reduction in the
personal tax rate (from 20 to 14
percent).
After-tax wages and
dividends increase by 7.5 percent,
while tax revenue (#92) decreases
by almost 20 percent. There is no
multiplier effect within the
submodel because the reinforcing
feedback loop from income to
spending is outside this submodel.
Figure 41. Income Distribution Submodel Test
shock: 30 percent cut in personal tax rate
MacroLab: The Model 49
5.7 Consumption Submodel
The focus now shifts to the nominal, demand side of the model economy. As both the
overview and detailed structure in Figure 42 indicate, the inputs to the consumption
submodel are disposable income (after-tax wages and dividends plus transfer payments) and
interest rates. Mankiw (ch.15) acknowledges and McConnell/Brue (ch. 9) emphasizes that
personal consumption is largely determined by personal disposable income, and both note
that a decrease in interest rates has a positive impact on consumption. Changes in wealth,
particularly reflected in changes in the value of homes and financial investment portfolios,
also affect consumption, but that influence is not included in the current version of
MacroLab.
Consumption Submodel
Figure 42
MacroLab: The Model 50
Consumption Submodel Equations
Left Side of Equation
98
Right Side of Equation
nominal consumption(t - dt) + (chgs in nominal
consumption) * dt
units
$/year
nominal consumption(t)
INIT historical = historic real C
INIT experimental = indicated nominal consumption
99
chgs in nominal
consumption
100
indicated nominal
consumption
101
time to adjust consumption
to income
102
propensity to consume
103
average propensity
to consume(t)
(indicated nominal consumption - nominal consumption) /
consumption adj time
$/yr/yr
disposable income * propensity to consume
$/year
2.5
years
average propensity to consume * smth1(interest rate effect
on consumption,time to adjust consumption to interest
rates)
1/1
average Propensity to Consume(t - dt)
1/1
INIT experimental = (wages & dividends+business saving +
taxes -investment -govt purchases) / (disposable income)
104
interest rate effect on
consumption
1+((interest rate - init(interest rate)) / init(interest rate)
*interest rate elasticity of consumption)
1/1
105
interest rate elasticity of
consumption
-interest elasticity of saving / (average propensity to
consume / (1-average propensity to consume))
1/1
106
interest rate elasticity of
saving
.2
1/1
107
time to adjust consumption
to interest rates
.5
years
108
nominal personal saving
disposable income - nominal consumption
$/year
historic real C
interest rate
historic nom consumption
historic disposable income billions
wages & dividends
business saving
taxes
investment
govt purchases
disposable income
Data Sector
Interest Rate Sector of Banking Submodel
Data Sector
Data Sector
Income Distribution Submodel
Income Distribution Submodel
Income Distribution Submodel
Capital Submodel
Government Submodel
Income Distribution Submodel
Figure 43. Consumption Submodel Equations
A key feature of this submodel is its incorporation of the well-documented
phenomenon of consumption smoothing (Fisher, 2001). Consumer spending in one period is
not determined solely by income in that period. Instead, as Friedman’s “permanent income
hypothesis” suggested fifty years ago, consumers appear to adapt their spending gradually to
changes in income. MacroLab’s default assumption for the average time to adjust
consumption to income (#101) is based on Friedman’s (1957, p. 229) conclusion that
MacroLab: The Model 51
Permanent income for the community as a whole can be regarded as a weighted average of
current and past incomes, adjusted upwards by a steady secular trend and with weights declining
as one goes farther back in time. The average time span between measured incomes averaged and
current permanent income is about 2.5 years.4
Of course, such an assumption does not mean that consumers wait 2.5 years to change their
spending after a change in income. Indeed, the first-order delay function (used throughout
MacroLab) generates the greatest rate of change in the output variable (e.g., nominal
consumption, #98) immediately after a change in the input variable (e.g., indicated nominal
consumption, #101). The rate of change slows after the initial response, however, as the
exponential averaging process used here—equivalent to Friedman’s geometric weight
averaging process (Glahe 1973)—puts less weight on previous inputs “as one goes farther
back in time.” As is the case with all key parameters, the consumption adjustment time can
be varied by the user at the interface level of MacroLab and different income smoothing
times can be tested.5
The propensity to consume (#102) is based on a reference value (average propensity
to consume, #103) and the interest rate effect on consumption (#104). When the model is in
historic mode, the average propensity to consume is based on historical data. In experimental
mode, the value is established so that the model is initialized in equilibrium, a condition in
which investment equals personal saving plus business saving and government spending
equals tax revenue. In the stand-alone consumption submodel, the average propensity to
consume is set at .90, but a pull-down menu permits variations in that assumption. The
marginal propensity to consume is not a parameter in the model; rather, it is determined
endogenously by the propensity to consume and the consumption adjustment time. Thus, the
marginal propensity to consume varies and its value depends on when the measurement is
taken. When measured over the period following an income shock, it will be smaller
immediately after a change in income but will approach the average propensity to consume as
the model approaches equilibrium.
The other key influence on consumption in this submodel is the change in interest
rates. Wright (1969) estimated the interest rate elasticity of saving (IRES, #106) to be .20.
Given the IRES and the average propensity to consume (APC, #103), the interest rate
elasticity of consumption (IREC, #105) can be calculated as follows:
IREC = - IRES / (APC/(1-APC))
which yields, for example, a default value of -.022 for the interest rate elasticity of
consumption in MacroLab when average propensity to consume is .90 and the interest rate
elasticity of saving is .20. With these parameter values, consumption would increase by
about 1 percent (0.0089) if interest rates fell by 40 percent (e.g., from 5 to 3 percent). The
effect is small compared to the effect of income, but it is does cause consumption to decrease
4
The same assumption was made by N. Forrester (1982) and N. Mass (1975).
Although MacroLab is not designed as a forecasting model, one test of the validity of its default parameter
assumptions is the extent to which its behavior matches historical data. Over five-year historical periods, the
model’s behavior correlates much better with US historical patterns when the 2.5 year consumption smoothing
time is used, compared to shorter time constants.
5
MacroLab: The Model 52
—and personal saving (#108) to increase—when interest rates rise, and conversely.
The results of a test of this effect are displayed in Figure 7.49. With an average
propensity to consume of .90, the impact would be difficult to discern if the graph were
drawn to scale for all variables.
Therefore, the test uses .80 for
the average propensity to
consume, and disposable income
is constant at $5 trillion/year.
Given the assumption of .20 for
the interest rate elasticity of
saving, the interest rate elasticity
of consumption would be -.05.
When interest rates drop from 5
to 3 percent, the propensity to
consume rises from .80 to .816,
Figure 44. Consumption Submodel Test
shock: interest rate decline from 5 to 3 percent
and the propensity to save drops
from .20 to .184. Thus, in the
graph, nominal consumption rises from $4.00 to $4.08 trillion/year, and nominal saving falls
from $1.00 to $0.92 trillion/year. In this example, the interest rate decline shifts $80 billion/
year from saving to consumption. (There is no multiplier effect because the feedback loop
from spending to income is outside the consumption submodel.6 ) When the more historically
accurate propensity to consume of .90 is used, the effect is reduced by more than half—
nominal consumption rises by about $40 billion/year.
The submodel is clearly sensitive to the assumption about average propensity to
consume, but that parameter is comparatively easy to estimate from historical data. The
time to adjust consumption to interest rates (#107) is highly uncertain, but the model is not
very sensitive to variations in that parameter. Also uncertain are the estimates of the interest
rate elasticity of saving and the adjustment time for smoothing consumption, and the model is
sensitive to changes in both parameters. Future refinements of MacroLab will include either
better estimates of both parameters or additional justification for the continued use of current
estimates.
6
If Wright’s (1969) estimate of the interest rate elasticity of saving included multiplier effects, then the .20
estimate is too high for use in the stand-alone submodel. However, it would still be appropriate when the full
model was running.
MacroLab: The Model 53
5.8 Government Submodel
Inclusion of a detailed government structure in the current version of MacroLab is part
of a long-range goal to endogenous many of government’s fiscal effects on the overall
economy. The most significant endogenous feature is the government budget, which grows
in proportion to tax revenue growth. The default assumption is that political leaders will
spend every dollar that comes in, and that spending will never decrease even when tax
revenue falls during a simulated recession. While clearly an oversimplification—after all, tax
cuts do happen—it appears to be the norm in the US. (It is possible to change that
assumption so that government must follow a balanced budget policy.) Another key
endogenous feature is the feedback effect of rising debt service payments on the division
between purchases and transfer payments. Government purchases—the residual spending
after social transfer payments and interest payments—tend to shrink as a portion of total
spending during periods of deficit financing, which is consistent with US historical trends.
Location of Government Submodel within the Main Model
Government Submodel
Figure 45
MacroLab: The Model 54
Government Submodel Equations
Left Side of Equation
109
government spending
110
nominal govt purchases
111
nominal transfer payments
112
Govt Budget(t)
Right Side of Equation
nominal govt purchases + nominal transfer pmts
$/year
Govt Budget - nominal transfer pmts
$/year
Govt Budget * social transfer pmts % of budget + interest
payments
$/year
Govt Budget(t - dt) + (govt budget chgs) * dt
$/year
INIT historical = historic real govt outlays
INIT experimental = indicated govt budget
113
govt budget chgs
114
balanced budget policy
0
1/1
115
budget adj time
1
years
116
budget gap
indicated govt budget - Govt Budget
$/year
117
indicated government
budget
taxes
$/year
118
If(balanced budget policy=0)then(max(0,budget gap/budget
adj time))
else(if(budget gap>0)then(budget gap/budget adj time)else
(budget gap/(budget adj time/3)))
Govt Debt(t - dt) + (govt borrowing - govt repayments) * dt
Govt Debt(t)
119
govt borrowing
120
govt repayments
121
avg govt bond maturity
122
$/year/
year
$
INIT historical = historic govt debt
INIT experimental = 5
government deficit + smth1(govt repayments,.08)
$/year
Govt Debt / avg govt bond maturity
$/year
5
years
government deficit
government spending - taxes
$/year
123
interest payments
Govt Switch*(Govt Debt*avg bond interest rate/100)
$/year
124
avg bond interest rate
if(Govt Debt>0)then(100*Cum Interest on Govt Debt/Govt
Debt)else(0)
1/year
125
govt bond rate
interest rate*.9
1/year
126
Cum Interest on Govt Debt
(t)
Cum Interest on Govt Debt(t - dt) + (interest additions interest subtractions) * dt
$
INIT = (interest rate/100) * Govt Debt
127
interest additions
128
interest subtractions
historic real govt outlays
taxes
interest rate
social transfer pmts % of budget
historic govt debt
if(govt borrowing>0)then((govt bond rate/100)*govt
borrowing)else(govt borrowing*(avg bond interest rate/100))
$/year
govt repayments*(avg bond interest rate/100)
$/year
Calculations Sector
Income Distribution Submodel
Interest Rate Sector of Banking Submodel
Calculations Sector
Calculations Sector
Figure 46. Government Submodel Equations
MacroLab: The Model 55
Still exogenous, however, is the reference budget division between purchases and transfer
payments, and also the highly simplified tax rates (in the data sector of the model).
Two principal inputs to the government submodel—taxes and interest rates—are
indicated in both panels of Figure 45. Government’s indicated budget (#117 in the equation
list) is equal to taxes, and the budget gap (#116) is the difference between the indicated
budget and the current budget (#112). When government is not following a balanced budget
policy (#114 = 0), then government budget changes (#113) can never become a negative
value; the net flow into the budget information stock will be zero (if taxes remain level or
decline) or a positive value. When the balanced budget policy is in effect, then the net
change in the budget can be positive or negative—the budget could shrink.
The exogenously influenced estimate of social transfer payments’ share of the budget is
added to the interest payments (#123) to determine nominal government transfer payments
(#111). The remainder of the budget goes to all other government purchases (#110) of goods,
services, and infrastructure. If total government spending (#109) exceeds taxes, then a deficit
(#122) exists and government borrows (#119) to finance the difference, and the debt (#118)
increases. The rate of repayments of principal (#120) depends on the average maturity
(#121) of government bonds. The debt is assumed to function on a rollover basis—
government borrows from Peter to pay Paul. The only way that the government debt can be
reduced is by running budget surpluses rather than deficits.
The interest payments (#123) are based on current debt and average interest rates (#124)
on that debt. A co-flow structure (Sterman 2000, ch. 12) is used to keep track of the average
interest rate. As government borrows, the interest obligations at that time are accumulated
(#127 and #126). When government pays off a bond holder, the average interest rate is
attached to that payoff in the interest subtractions outflow (#128). The significance of this
structure is that the average interest rate changes more slowly than the current rate (#125).
To illustrate the behavior of the government submodel, Figure 47 displays three
simulation experiments in which the submodel is shocked by a five percent change in tax
revenue. In panel A, taxes increase by five percent, which causes a five percent increase in
the government budget (under both balanced and unbalanced budget policies). With an
average budget adjustment time of one year, the complete adjustment takes a little more than
three years and a budget surplus exists during the transition period. During the budget
surplus period, the debt is reduced and interest payments fall slightly. The fall in interest
payments keeps transfer payments from rising quite as much as otherwise would have been
the case. Thus, government purchases grow by slightly more than five percent and transfer
payments grow by slightly less than five percent.
MacroLab: The Model 56
Panels B and C illustrate the
dynamics when tax revenue falls by five
percent.
In panel B, government is not
following a balanced budget policy, and
the budget does not decline when taxes
fall. Instead, a continuous deficit occurs,
and there is an increase in the debt and
interest payments. The rise in interest
payments causes transfer payments to
rise. However, since the government
budget is flat, government purchases
decline by an amount equal to the transfer
payments increase.
In panel C, government follows a
balanced budget policy. The five percent
reduction in taxes causes a five percent
reduction in the government budget, with
the adjustment time accelerated to
complete the adjustment within one year.
Both government purchases and transfer
payments decline by almost the same
amount. Due to the brief deficit during
the transition to a balanced budget,
however, the debt and interest payments
rise slightly, which causes transfer
payments to decline somewhat less than
government purchases.
Panel A: Taxes Increase by 5 Percent
Panel C: Taxes Decrease by 5 Percent, with
UNbalanced Budget Policy
Panel C: Taxes Decrease by 5 Percent, with
Balanced Budget Policy
Figure 47. Government Submodel Effects
of Change in Tax Revenue
MacroLab: The Model 57
5.9 Money Sector within the Banking Submodel
The banking submodel has two sectors, one for money and interest rates and the other
for monetary policy. Here, the focus is on the structure of the model’s banking system and
how it affects the money supply and interest rates. The next section describes the influence
of monetary policy on the banking system.
Location of Banking Submodel within Main Model
Money Sector of Banking Submodel
Figure 48
MacroLab: The Model 58
Money Sector Equations in Banking Submodel
129
Left Side of Equation
Right Side of Equation
units
deposits(t)
deposits(t - dt) + (making deposits + net deposits from RW making withdrawals) * dt
$
INIT historical = historic M2-historic currency
INIT experimental = initial M2*(1-initial currency to m2 ratio)
130
making deposits
Fed purchases of bonds+net lending rate+net deposits from
RW
$/year
132
making withdrawals
((deposits * currency deposit ratio)-currency) / currency adj
time
$/year
133
currency(t)
currency(t - dt) + (making withdrawals) * dt
$
INIT historical = historic currency
INIT experimental = initial M2*initial currency to m2 ratio
134
currency deposit ratio
135
currency adj time
137
interest rate effect on CD
ratio
smth1((1+interest rate effect on CD ratio)* reference
currency deposit ratio,.5)
2.5
1/1
years
GRAPH(smth1(loan rate / init(loan rate),3))
1/1
(0.00, 0.125), (0.2, 0.124), (0.4, 0.123), (0.6, 0.12), (0.8,
0.114), (1.00, 0.00), (1.20, -0.0165), (1.40, -0.027), (1.60,
-0.0315), (1.80, -0.0345), (2.00, -0.0375)
138
reserves supply(t)
reserves supply(t - dt) + (net reserve additions)*dt
$
INIT historical = historic bank reserves
INIT experimental = reserves demand
139
net reserve additions
net deposit chg
$/year
140
net lending rate
if(compliance adjustment<0)then(compliance adjustment)
else(bank lending - init(bank lending))
$/year
141
bank lending
(bank % of lending/100)*investment
$/year
142
bank % of lending
15
144
reserves demand
reserve ratio * deposits
145
reserve ratio
146
net deposit chg
making deposits - making withdrawals
147
excess reserves
reserves supply / reserves demand
147b
compliance adjustment
148
FF rate(t)
M2 required reserve ratio+excess reserve ratio
(reserves supply-reserves demand)/.04
reserves supply(t - dt) + (net chg in FF rate)*dt
1/1
$
1/1
$/year
1/1
$/year
1/yr
INIT historical = historic FF rate
INIT experimental = 4
149
net chg in FF rate
150
FF rate adj time
((init(FF rate)/excess reserves)-FF rate)/FF rate adj time
1/yr/yr
.04
years
MacroLab: The Model 59
151
loan rate(t)
loan rate(t - dt) + (net chg in loan rate) * dt
1/yr
INIT historical: historic prime rate
INIT experimental: FF rate+3
152
net chg in loan rate
153
loan rate adj time
154
borrowing & savings ratio
historic M2
historic currency
initial M2
initial currency to m2 ratio
historic bank reserves
historic bank% of investment loans
Fed purchases of bonds
historic FF rate
historic prime rate
net borrowing
Savings
M2 required reserve ratio
excess reserve ratio
net deposits from RW
investment
reference currency deposit ratio
(((borrowing & savings ratio/init(borrowing & savings_ratio))
*(FF rate+3))-loan rate)/loan rate adj time
1/yr/yr
.08
years
(net borrowing / init(net borrowing))/(Savings / init(Savings))
1/1
Data Sector
Data Sector
Data Sector
Data Sector
Data Sector
Data Sector
Policy Sector of Banking Submodel
Data Sector
Data Sector
Data Sector
Main Model
Policy Sector of Banking Submodel
Data Sector
Data Sector
Main Model
Data Sector
Figure 49. Money Sector Equations within the Banking Submodel
In their chapters on money and banking, Mankiw (ch. 11) and McConnell/Brue (ch. 14)
emphasize the process by which the banking system creates multiple expansions or
contractions of the money supply and affects the supply and price of credit for both
households and business firms. When only the Simple Private Sector of MacroLab is
functioning, the money supply is fixed, and interest rates are determined simply by the
relative supply of loanable funds (the Savings stock at the main model level) and the demand
for those funds (the investment outflow from savings). When the Banking Sector is
activated, however, the money supply can grow (and decline) as banks make loans, and
interest rates receive an additional influence—banks’ incentives to make loans.
Before describing the way the money sector works, some unusual aspects of Figure 48
should be explained. As previously mentioned, most of the exogenous inputs to these
submodels would be endogenous connections if the full model were running. Examples are
“net borrowing” and “Savings.” The Savings stock receives the net deposit change from the
money sector, and Savings is the loanable funds influence on interest rates in the money
sector. Thus, a loop exists. Likewise, net borrowing—which includes investment—affects
interest rates in the money sector, but the interest rates affect the borrowing; another loop
exists. Moreover, as we saw in the main model, investment is an outflow from the stock of
Savings; without an inflow (e.g., from personal and business saving), Savings would be
drained in the monetary sector. Where to draw the line between endogenizing relationships
and maintaining stand-alone submodels is a difficult choice. In this case, investment was
needed as a response variable in the monetary sector; otherwise, the change in interest rates
would not affect lending rates. Since Savings could not be properly used to represent a
supply influence on loan rates, net borrowing could not be used as the corresponding demand
influence. However, both variables are displayed on the diagram in Figure 48 as a reminder
MacroLab: The Model 60
that they do influence interest rates when the full model is running. Let us now focus on
some essential structure in the money sector of the banking submodel.
Near the bottom of the diagram in Figure 48, the deposits and currency stocks (#129
and #133 in the equation list) comprise the money supply, M2. Leaving currency aside for
later discussion, consider the simple feedback loop structure in Figure 50. When customers
make deposits (#130), that creates both liabilities and assets for a bank. The liability is the
total value of customer accounts, while the assets are the bank’s reserves. A certain fraction
of reserves (#145) is required by law and by prudent banking practice to be set aside,
unavailable for lending. The set-aside amount is called reserves demand (#144). When the
total supply of bank reserves (#138)
exceeds reserves demand, an excess (#147)
exists. Idle excess reserves earn no interest,
so banks have an incentive to reduce the
reserves supply to the level of reserves
demand. When excess reserves increase,
competitive banks will offer incentives to
attract loan customers. One incentive, of
course, is the interest rate on the loans.
When excess reserves increase, that puts
downward pressure on interest rates, ceteris
paribus.
The feedback diagram uses the single
term “interest rates.” In Figure 48, two
interest rates are represented—the Fed
Funds rate (#148) and the loan rate (#151).
Figure 50
The Fed Funds rate is most immediately
affected by discrepancies between reserves
supply and demand. The Fed Funds market is the interbank loan market for commercial
banks that have either a surplus or deficit of reserves. If excess reserves exist for the banking
system as a whole, individual banks with excess reserves will tend to lower their asking price
for short-term loans; otherwise, banks in need of reserves will turn to other short-term loan
markets. Reserves that are abundant and that are losing potential as interest-bearing assets in
the Fed Funds market will also be offered to the bank’s personal and commercial loan
customers at lower-than-normal loan rates. Also, the “other short-term loan markets” will be
moving in the same direction as the Fed Funds market, as attempts are made to compete for
borrowers needing reserves.
The lower interest rates will attract more loan customers and net lending (#140) will
increase. Assuming for a moment that the loans are not taken out of the banking system in
the form of cash, each new loan gets placed in an existing or new customer account, and the
banking system’s liabilities grow. The reserves loaned out simultaneously add and subtract to
the banking systems’ supply of reserves, as suggested by the R1 and C1 loops in Figure 50.
The reserves supply remains unchanged but the reserves demand grows as the reserve ratio is
applied to a larger stock of deposits. Whatever excess reserves existed before, it is somewhat
smaller now. As the process continues and the demand for reserves rises to meet the supply,
MacroLab: The Model 61
the excess disappears and upward
pressure on interest rates appears—first,
on the Fed Funds rate and eventually on
all other loan rates. Counteracting loop
C2 in Figure 51 illustrates the process.
With each round of new deposits, the
reserves demand grows, the excess
reserves shrinks, interest rates rise, new
lending slows down, and fewer new
deposits are made.
In the meantime, however, the
initial quantity of excess reserves has
generated an increase in the money
supply, defined as “deposits” in Figures
50 and 51 since we have been assuming
Figure 51
zero currency.
If we drop that
assumption, we can see in Figure 52
that the potential for money supply growth described above is limited by loops set in motion
by the public’s demand for cash.
About ten cents of every dollar deposited in M2 accounts is eventually withdrawn in the
form of cash. As loop C3 in Figure 52 suggests, for a given currency-to-deposit ratio, more
deposits means more withdrawals (132), and more withdrawals means a lower level of
deposits. Follow loop R2, and a reinforcing process can be seen. The lower deposit level
reduces reserves demand, which increases excess reserves and lowers interest rates. Lower
interest rates provides less incentive to put extra cash in bank accounts and more incentive to
hold cash for convenience; thus, the currency-to-deposit ratio rises (#137 and #134) and leads
to an even greater rate of cash withdrawals from the banking system.
The withdrawals also reduce the net
deposit rate (#146) and the net additions to
the supply of reserves (#139). Thus, the
cash withdrawals reduce both the demand
for reserves (R2 loop) and the supply of
reserves (C4 loop). What is the net effect?
Every dollar of cash withdrawn is a dollar
of reserves supply removed from the
system. Each of those dollars “lost,”
however, reduces the reserves demand by
only a fraction. Thus, the net effect is to
reduce the supply of reserves much more
than the demand, and that reduces the
potential for excess reserves to be loaned
and new deposits created. The currency
withdrawal process, then, limits the
potential growth in the money supply. But
Figure 52
MacroLab: The Model 62
there is a limit to the limit. The C4 loop eventually raises interest rates and encourages more
deposits and a lower currency-to-deposit ratio.
To test whether the structure described
above produces such behavior, MacroLab’s
money sector was shocked with an injection
of $100 billion, and the results are displayed
in Figure 53. In the top panel, the feedback
loop connecting interest rates and the
currency-to-deposit ratio has been cut, and
the currency-to-deposit ratio remains
constant.
The loan interest rate falls
immediately after the shock, and then rises
steadily.
In the middle panel, the same shock is
administered, but the feedback loop is
reactivated. When the interest rate falls, the
currency-to-deposit ratio rises. Moreover,
the additional cash withdrawals accelerate
the interest rate rebound, but that eventually
encourages more saving and the currencyto-deposit ratio comes back down.
In
addition, the feedback effect stabilizes
interest rates.
The bottom panel in Figure 53 shows
the effects on the money supply. The blue
curve corresponds to the top panel—when
the currency-to-deposit ratio remains low
because there is no feedback effect from the
interest rates. The red curve corresponds to
the middle panel, when the currency-todeposit ratio rises. As expected in the latter
case, the growth in the money supply is
limited by the additional cash withdrawals.
No Interest Rate Effect on Currency-to-Deposit Ratio
Feedback Loop Connects Interest Rate
and Currency-to-Deposit Ratio
More Cash Withdrawals Limited Growth in the Money
Supply
Figure 53
In this discussion of the structure and
behavior of the money sector submodel, no explanation was given for what might have
precipitated such shocks to the system. In the next subsection, a simple monetary policy
model will illustrate one source of such shocks.
MacroLab: The Model 63
5.10 Monetary Policy Sector within the Banking Submodel
In this subsection, a very simple model of monetary policy is presented, as part of a
long-range plan to endogenize much of government economic policy making. The model
follows the textbook approach to open market operations by the Federal Reserve System (the
“Fed”). As explained in Mankiw (ch. 11) and McConnell/Brue (ch. 15), the goals of the
Federal Open Market Committee (FOMC) include economic growth, low unemployment,
and stable prices. When economic conditions warrant action with respect to these goals, the
FOMC authorizes the staff of the New York Federal Reserve Bank to engage in open market
buying and/or selling of US government bonds with the objective of adjusting interest rates to
desired levels and influencing aggregate demand accordingly. Figure 54 displays the stockand-flow structure responsible for such decision-making and action within MacroLab.
Figure 54. Monetary Policy Sector within the Banking Submodel
Two of the inputs to this sector—inflation and the unemployment rate—are among the
economic indicators monitored by the FOMC in its deliberations. The outputs are two
policy instruments available to the Fed: (1) the required reserve ratio and (2) open market
operations. Finally, at left, note the three blue information inputs from the money sector.
Information about the Fed Funds rate and the supply and demand for reserves provides the
data needed to formulate an action plan to pursue inflation and unemployment goals. The
general strategy is to decide whether interest rates should be higher or lower, and to
manipulate the supply of bank reserves so as to influence the Fed Funds rate directly, the loan
rate indirectly, and aggregate demand ultimately.
MacroLab: The Model 64
Policy Sector Equations within Banking Submodel
Left Side of Equation
Right Side of Equation
155
desired % chg in FF rate =
if(FF Rate=0)then(0)
else((target FFR-FF Rate)
/ FF Rate)
156
target FF rate(t) =
target FFR(t - dt) +(net chg in target FFR)*dt
1/1
1/year
INIT = FF Rate
157
net chg in target FFR =
(indicated target FF rate - target FF rate)
/ target FFR adj time
1/yr/yr
158
target FFR adj time =
0.25
years
159
indicated target FF rate =
init(target FF rate)
* (inflation effect on target FFR
/init(inflation effect on target FFR))
* (UR effect on target FFR
/init(UR effect on target FFR))
1/year
160
inflation effect on target FFR
GRAPH(if(inflation goal=0)then(perceived inflation by Fed/.
25)else(perceived inflation by Fed/inflation goal))
1/1
(0.00, 0.54), (0.333, 0.58), (0.667, 0.62), (1.00, 0.74), (1.33,
1.28), (1.67, 1.98), (2.00, 4.00)
161
UR effect on target FFR
UR goal/perceived UR by Fed
162
inflation goal =
H: 3
E: 0
163
UR goal =
5
1/1
164
perceived inflation by Fed
smth1(inflation,inflation perception adj time)
1/yr
165
perceived UR by Fed
smth1(unemployment rate, UR perception adj time)
1/1
166
inflation perception adj time
0.25
years
167
UR perception adj time
0.25
years
168
Fed purchases of bonds
((reserves demand-(1+(desired % chg in FF rate))*reserves
supply)/compliance time))
$/year
169
compliance time
2
weeks
170
M2 required reserve ratio
.01
reserves supply
reserves demand
inflation
unemployment rate
FF rate
Money Sector of Banking Submodel
Money Sector of Banking Submodel
Data Sector
Labor Submodel
Money Sector of Banking Submodel
Figure 55. Equations in Policy Sector of Banking Submodel
1/1
1/year
1/1
MacroLab: The Model 65
The focus in this subsection is on open market operations since that is the only policy
tool that is formulated endogenously within the current version of MacroLab. The required
reserve ratio can be varied exogenously, and its default value—.01—is the approximate
average ratio of required reserves to M2 over the past twenty years in the US. For most of
that time, non-checkable deposits have had no reserve requirement, and checkable deposits
(those in M1) have had a weighted average requirement of slightly less than ten percent.
Below, we develop a general outline of the policy development process and then
illustrate how that process is formulated in MacroLab. To the extent possible, we want to
formulate decision rules in the model that evoke visions of real policy makers thinking and
acting in real time. To that end, let us imagine what the policy makers know and how they
might react to a development that calls for a change in policy. The following discussion
parallels the line of reasoning in Table 15.3 of McConnell/Brue.
Figure 56. Structuring the Policy Problem
We begin by assuming the policy makers believe the hypotheses implicit in the links in
the top panel of Figure 56. That it is to say, they believe that an increase in interest rates
reduces nominal aggregate demand, ceteris paribus. Moreover, they are aware of the short
run trade-off between inflation and unemployment resulting from sharp changes in nominal
aggregate demand (Mankiw’s fourth principle, discussed in section 3.4). They also know that
they should adopt a target interest rate based on the links in the bottom panel, and then act
accordingly. For example, a rise in inflation suggests the policy of raising interest rates and
curbing demand, while a rise in unemployment suggests the opposite policy. If the implicit
MacroLab: The Model 66
interest rate target falls, the policy makers know they should buy more bonds in order to
depress interest rates (bringing them closer to the interest rate target) and boost demand.
Finally, they are painfully aware of the feedback consequences of their actions, as suggested
by the loops C7 and C8. A balanced policy approach is one that recognizes the trade-off
between unemployment and inflation. Nevertheless, it is inevitable that the interest target
will change in the future as a result of policy actions in the past.
The first modeling challenge, therefore, is to write equations that enable policy makers
to become aware of the economic conditions of concern to them, and the next step is to write
a decision rule for the conduct of open market operations. We begin with the exogenous
inputs that represent conditions in the economy—the information about inflation and
unemployment. Policy makers do not know the current level of unemployment or the current
rate of change in prices; they only know what they see in data collected last month, and even
then they are assumed to take some time to adjust their perceptions. In the model, the default
assumption is that the average time delay in updating those perceptions (#165 and #166) is
approximately three months. Like most time constants in MacroLab, these assumptions can
be varied at the interface level of the model.
The policy makers in the model compare their perceptions with their goals for
unemployment and inflation. The default goal for the unemployment rate (#163) is 5 percent,
roughly the average in the US over the past twenty years and close to the current CBO
estimate of the “natural” rate of unemployment. The default inflation goal (#162) is 3 percent
unless the model is in a no-growth experimental mode, in which case the inflation goal is
zero. When the unemployment rate changes, the impact on policy (#161) is assumed to be
proportional to the relationship between the perceived unemployment rate and the goal.
When inflation changes, the impact (#160) is presumed to be nonlinear and
disproportionately greater at higher levels of inflation, as Mankiw (2002) suggests.
The impact of perceived inflation and unemployment are compared with their initial
impacts at the beginning of the simulation run, and “effect” ratios are computed. The two
ratios are given equal weight in equation #159, and multiplied times the initial value of the
Fed Funds rate. When the ratios are both equal to one, no policy change occurs. When the
product of the ratios is greater than one, the target Fed Funds (#156) rate rises, and
conversely. A desired percentage change in the Fed Funds rate (#155) is used in the
calculation of the volume of Fed bond purchases (#168). The formulation of equation #155
is similar in principle to the so-called “Taylor Rule” (Taylor, 1993) and adaptations such as
the “Mankiw Rule” (2002). In the current version of the model, the equation is not based on
econometric estimates of the Fed’s policy response function, but an illustration later in this
subsection makes use of such estimates and improves the “fit” between the simulation results
and historical data.
This description of the model’s sequential decision rules has taken us from “interest rate
target” to “Fed purchases of bonds” in the bottom panel of Figure 56. To get to interest rates
and, ultimately, to aggregate demand, it is necessary to overlay the Fed purchases with the
money sector diagram, which is accomplished in the two panels of Figure 57.
MacroLab: The Model 67
Figure 57. Feedback Loops in the Money Sector Resulting from Fed
Purchases of Bonds
When the Fed buys bonds, the sellers receive an increase in their bank deposits, and
their banks automatically receive a credit to their reserve account at the regional federal
reserve banks. In one respect, the effects of the deposits triggered by the Fed’s actions are
similar to the effects examined earlier in Figures 50 and 51. The deposits increase reserves
demand by an amount determined by the reserve ratio. The deposits also increase reserves
supply by the full amount. The significant difference, however, is that money the bond
sellers receive from the Fed does not simultaneously drain the reserves of other banks in the
system. It is “new” money, and creates an immediate increase in excess reserves that will
have the effects on interest rates that we examined earlier.
Once the FOMC has established a target Fed Funds rate and an initial shock to the
system occurs, the effect on the Fed Funds rate is almost immediate, and other interest rates
respond over a period measured in a few weeks rather than a few months. That sets in
motion a series of feedback effects that could—if unchecked—counteract the initial change in
the Fed Funds rate. For that reason, the FOMC authorizes Fed staff to enter the open market
each week to buy or sell bonds, as necessary to offset market forces that would push the
banks’ reserves supply in a direction that could cause the Fed Funds rate to depart from the
target rate. The policy receives constant maintenance. The formulation of that maintenance
MacroLab: The Model 68
is achieved in equation #168. Even when there is no change in the desired Fed Funds rate,
the reserves supply and demand ratio established by the initial intervention is maintained by
that equation.
Figure 57 is not the end of the story, however. The inflation and unemployment
conditions need to receive the effect of the change in interest rates, and Figure 58 illustrates
the feedback effect. The top panel of Figure 58 maintains consistency with previous
diagrams but is difficult to read. The bottom panel abstracts out just the feedback loops C7
and C8, and the path of influence becomes clear. The loop is closed between the Fed’s
perception of economic conditions, formulation of a policy to address those conditions, and
the impact on those conditions (plus the updated perceptions as conditions change).
Figure 58. Closing the Loop Between Fed Policy and the Impact on Inflation and
Unemployment
The first behavioral illustration of these structural explanations demonstrates the
direction of the policy response to changing economic conditions. In addition, it highlights
the issue of perception delay. The shock test demonstrates the policy response to inflation and
unemployment. It also mimics the response of the economy to the policy. Since the
economic conditions are exogenous to this submodel, there can be no actual effect from the
model. However, by using a sine wave input function, it gives the policy rule a moving
target, enabling observation of how continuous changes in economic conditions trigger policy
changes in the model.
MacroLab: The Model 69
Panels A1 and A2 in the top row of Figure 59 illustrate the response of the Fed Funds
rate to a sine wave of changing inflation. Note that the interest rise moves (with a lag) in the
same direction as inflation, as the structure requires.
A1: Average Inflation Perception Delay: 1 Year
A2: Average Inflation Perception Delay: 3 Months
B1: Avg. Unemployment Perception Delay: 1 Year
B2: Avg. Unemployment Perception Delay: 3 Months
Figure 59. Delayed Perceptions of Economic Conditions Affect Fed Funds Rate Timing
The bottom row (B1 and B2) illustrates the sine-waving unemployment rate and the
opposite-direction movement of the interest rate (with a lag). When the unemployment rate
rises, the Fed Funds rate falls, and conversely.
The difference between the panels A1 and A2 (and also between B1 and B2) is the
length of the perception time assumption. In A1 and B1, the policy makers are assumed to
get their information late or update their perceptions slowly, or both—the average delay is
one year. In both panels A1 and B1, note that the interest rate response tracks the perceived
condition in the economy fairly closely, but lags the actual condition considerably. In panel
A1, the interest rate response to rising perceived inflation occurs at a time when actual
inflation has already peaked and turned down. Such an out-of-phase policy is akin to “too
much, too late” and could push the economy into a recession. (A recession does not occur in
panel A1 because the inflation pattern is driven by the sine wave input and not by the interest
rate.) In panel A2, the submodel used the default assumption of a three-month perception
delay, and the interest rates rise and fall in a more timely fashion. Panels B1 and B2 illustrate
the same point with regard to the unemployment rate.
MacroLab: The Model 70
The sine wave exogenous input is one of several exogenous test inputs that could be
used to shock the model. In Figure 60, actual historical data have been used. The inputs to
the exogenous model variables “inflation” and “unemployment rate” are the monthly
inflation and unemployment rate data from the US over the twenty-year period since 1986.
Thus, it is possible to compare the behavior of interest rates in the model with the historical
interest rates, when both are responding to the same economic data.
Figure 60. Interest Rate “Fit” with Historical Interest Rates
When Historical Inflation and Unemployment Rate are Inputs to Banking Submodel
Whether it is a “good fit” or not is for readers to decide. There appears to be an upward
bias in the MacroLab interest rate response, or it could be that other forces in the historical
economy produced a downward bias in actual interest rates, unrelated to monetary policy.
Or, it could be that the crude policy decision rule in the model is only capable of capturing
general up-or-down trends. For most pedagogical purposes, that will be sufficient make the
point.
The results of another test of the model’s response to the same historical input data are
presented in Figure 61. This time, instead of equation #157, the so-called “Mankiw Rule”
was used to calculate the target Fed Funds rate. Mankiw (2002) performed a regression
analysis of historical data on the Fed Funds rate, inflation, and unemployment during the
1990s. His equation
Fed Funds Rate = 8.5 + 1.4 * (core inflation – unemployment)
fits the data for that period very well, with an adjusted R2 of .85. His equation was
substituted into the “net chg in target FFR,” and “perceived inflation by Fed” and “perceived
UR by Fed” replaced “core inflation” and “unemployment.” Use of the Mankiw’s equation
improves the correlation between the behavior of the model’s interest rates and historical
interest rates.
Figure 61. Use of the Modified “Mankiw Rule” in the Setting of the Target Fed Funds Rate
When Historical Inflation and Unemployment Rate are Inputs to Banking Submodel
MacroLab: The Model 71
In his discussion of the equation, Mankiw (2002, p. 37) says, “this tight fit has
profound implications for understanding monetary policy. … The Fed raises interest rates in
response to higher inflation to cool the economy [and] responds to high unemployment by
cutting interest rates to stimulate aggregate demand.”
His regression model does provide empirical support for hypotheses about the
motivation of monetary policy makers, and that is important when writing decision rule
equations. However, the regression model provides no glimpse into the process of
converting policy motivations into policy outcomes over time. For that purpose, a different
model is needed. The behavior of a dynamic process model should reflect actual history, but
it should have the added benefit of clarifying how and why such behavior developed over
time. Feedback diagrams based on stock-and-flow structure, when coupled with simulation
capability, enable connection of structure and behavior. That has profound implications for
understanding policy.
MacroLab: The Model 72
5.11 Exchange Rate Submodel
In the “gains from trade” discussion in section 7.3.6, the exchange rate issue was
postponed. Now we consider it. Mankiw (2007, chs. 13-14) and McConnell/Brue (2005, ch.
21) emphasize three influences on the exchange rate between two currencies: relative prices,
relative aggregate demand, and relative interest rates, summarized as follows (with the
obligatory ceteris paribus qualification for each):
1. When US prices rise more than RW prices, the value of the dollar falls.
2. When the US increases its imports from the RW more than the RW increases its imports
from the US, the value of the roller rises and the value of the dollar falls.
3. When US interest rates rise more than interest rates in the RW, the value of the dollar rises.
The feedback loop diagram in Figure 62 is derived from the exchange rate stock-andflow structure in Figure 63. Both diagrams—and the underlying equations in Figure 64—are
consistent with the three basic hypotheses listed above. In the feedback diagram, an increase
in US prices reduces RW demand for US goods (expressed first in foreign currency and then
divided by the exchange rate to convert to US currency). That reduces US net exports,
increases the relative supply of dollars in the RW, and lowers the exchange rate. To see the
representation of the second hypothesis, assume US demand increases. The increase in US
payments for imports would decrease US net exports, increase the relative supply of dollars
in the RW, and reduce the exchange rate. The third hypothesis is evident when an increase in
US interest rates is assumed. That increases the net capital flow to the US, as dollardenominated securities appear more profitable. The resultant decrease in the relative supply
of dollars in the RW raises the exchange rate.
Figure 62. Exchange Rate Determined by Relative Change
in Supply of Dollars in the RW (and Rollers in the US, not shown)
MacroLab: The Model 73
Figure 63. Exchange Rate Submodel
The feedback loop is visible in the stock-and-flow structure of the submodel. In Figure
63, follow the links from Xchg rate $ (#176 in the equation list below) to nominal RW pmts
for imports $ (#187) to US nominal net exports $ (#182) to relative chg $ supply (#179) and
back to the exchange rate. The stock-and-flow diagram also includes the parallel feedback
loop running through the stock of foreign currency in the US (® in US, #184).
The relative supply equation (#179) compares both currency stocks to compute a
relative change. Despite the word “supply” in the equation name, equation #179 is actually
measuring net change in the stocks. The net change is due to inflows (net export payments by
the US) and outflows (net capital inflows to the US), which are measures of supply and
demand, respectively. Thus, relative supply and demand for both currencies drives changes
in the exchange rate.
The logic of the three hypotheses is also visible in the stock-and-flow structure. The
increases in both US prices (top right) and US demand (left) put downward pressure on the
exchange rate by reducing US net exports and the demand for dollars needed for payments.
The mechanism for the interest rate hypothesis is the capital inflow of dollars to the US (and
out of the RW). The hypotheses are also revealed by scrutiny of the relevant equations in
Figure 64, but readers who are tired of equations by now may want to skip straight to the
simulation examples, where the submodel tests for the hypothesized behavior.
MacroLab: The Model 74
Exchange Rate Submodel Equations
Left Side of Equation
176
Xchg rate $(t)
Right Side of Equation
Xchg rate $(t - dt) + (Xchg rate chgs) * dt
units
®/$
INIT = 1
177
Xchg rate chgs
178
adj time for Xchg rate
179
relative $ supply
180
$ in RW(t)
((init(Xchg rate $) * (1/relative $ supply)) -Xchg rate $) / adj
time for Xchg rate
®/$
/ year
.02
years
($ in RW / ® in US) /(init($ in RW) / init(® in US))
1/1
$ in RW(t - dt) + (- US net capital inflow $ - US nominal net
exports$) * dt
$
INIT $ in RW = 1
181
US net capital inflow $
$ in RW*US relative interest rate
$/year
182
US nominal net exports$
nominal US receipts for exports $ - nominal US pmts for
imports $
$/year
183
US relative interest rate
(interest rate-interest rate RW) / interest rate RW
184
® in US(t)
1/1
® in US(t - dt) + (- RW net capital inflow ® - RW nominal net
exports ®) * dt
®
INIT ® in US = 1
185
RW net capital inflow ®
-US net capital inflow $ * Xchg rate $
®/year
186
RW nominal net exports ®
-US nominal net exports$ * Xchg rate $
®/year
187
nominal RW pmts for
imports $
nominal RW pmts for imports ® /Xchg rate $
$/year
188
nominal US pmts for imports
®
nominal US pmts for imports $ * Xchg rate $
®/year
189
nominal US receipts for
exports $
nominal RW pmts for imports $
$/year
190
US unit import cost $
experimental
price index RW / Xchg rate $
1/1
191
US unit export cost ®
price index * Xchg rate $
1/1
192
real imports into US
H: historic real imports/1000
$/year
E: nominal US pmts for imports $ / US unit import cost $
experimental
193
real imports into RW
interest rate
interest rate RW
nominal RW pmts for imports ®
nominal US pmts for imports $
price index
price index RW
historic real imports
nominal RW pmts for imports ® /
US unit export cost ®
Main Model
Main Model RW
Data Sector
Data Sector
Main Model
Main Model RW
Data Sector
Figure 64. Exchange Rate Submodel Equations
®/year
MacroLab: The Model 75
Figure 65 shows the results of the three separate simulation tests of the exchange rate
hypotheses discussed above. The test results in the top panel came from the exchange rate
submodel. The full model generated the results in the bottom panel. In each test for both
models, there was a 10 percent step increase in one input variable. In each test of the
submodel, all other exogenous input variables remained constant. In the full model, all
variables were free to move after the shock.
Submodel Tests
Full Model Tests
Figure 65. Separate Tests of Each Hypothesis
The isolated tests in the submodel show the expected results. The exchange rate moves
unmistakably in the “right” direction during each test. The results in the full model are not
inconsistent with the hypotheses, but the magnitudes are much smaller than in the submodel
experiment. In one case—the interest rate shock—a microscope is needed to see the slight
rise in the exchange rate, and even that effect is temporary as the interest rate (on a separate
graph) soon settles down near its initial value. The price effect is sharp but temporary, as
price also returns to its initial level. Only the demand shock has a sustained effect, but it also
seeks a return to its original equilibrium value as the simulation ends in the tenth year.
MacroLab: The Model 76
5.12 The Value of Simulation
Throughout this chapter, a caveat has been repeated: When submodels contain
exogenous inputs that are endogenous to the full model (and endogenous in real economic
systems), it is likely that the behavior of the submodel, when shocked, will be somewhat
different from the behavior of the full model if shocked the same way. The significance of this
point is amplified when there are several exogenous inputs that interact with each other when
endogenized. The tests of the exchange rate hypotheses in the submodel and the full model
illustrate what can happen.
The full model tests, of course, do not mean that the hypotheses are wrong. An axiom
among modelers is that “all models are wrong, but some are useful.” Both the full model and
the submodel are certainly wrong in the sense of being only simplified representations of
reality. The exchange rate results in the full model might mean the model needs structural
adjustment or better parameter estimates. However, a different interpretation is possible,
especially since the submodel produces the hypothesized behavior in magnitudes and patterns
that are easy to see and interpret. When “everything else” is literally held constant, the
hypotheses are supported, and that’s all the hypotheses claim.
When the entire system is subjected to a shock, system-wide hypotheses are necessary
to take into account the interaction and feedback effects. Such hypotheses are difficult to
develop with words and graphs. Feedback diagrams can be helpful in the development—but
not the testing—of such hypotheses. The value of a simulation model in hypotheses testing
has been illustrated in the exchange rate hypotheses examples. Such a model must be
accessible, however, to students and scholars from diverse backgrounds and with diverse
learning styles and preferences. The next—and final—document in this thesis introduces the
interactive learning environment (ILE) of MacroLab. The examples provided in the ILE
document are intended to illustrate how the feedback diagramming approach is integrated
with the simulation experiments when teaching macroeconomics.
MacroLab: The Interactive Learning Environment 77
MacroLab: The Interactive Learning Environment
This final chapter is intended as a
simple guide to using the interactive learning
environment (ILE) of MacroLab. As such, it
has two purposes.
First, it aims to
demonstrate how students use the ILE in a
macroeconomics course. The focus will be on
how the ILE integrates feedback loop analysis
and simulation activities. The second purpose
of the chapter is to provide instructions for
readers interested in exploring the ILE and
experimenting with simulation options.
The ILE and its underlying system dynamics model of nearly 500 equations have been
developed with system dynamics software called STELLA (http://www.iseesystems.com). In
general, a file created with a STELLA application has three levels of information: the
interface level (where the ILE is visible), the model level (where the stock-and-flow structure
is constructed), and the equation level (containing a comprehensive list of equations in the
model). Beginning with version 9 of STELLA, navigating between the levels is accomplished
by simply clicking on left-hand side tabs. Earlier versions of the software have small black
triangles pointing up or down to indicate options for moving to a higher level (e.g., the
interface) or a lower level (e.g., the equations).
1. Layout and Navigation
Figure 66 displays a site map of the
interface level of the MacroLab file.
The
site map is always available to the user who
gets lost. To go to the site map, merely click
on the question mark (?) button at the bottom
of any page at the interface level. Each
button on the site map is a link to the page
indicated by the button name.
From the Title Page, the user should
advance to the Overview page by clicking
obvious “next” buttons. Figure 67 displays
the Overview page and its links to the
sections of the ILE devoted to the four main
sectors of the model: the simple private
Figure 66. Site Map for MacroLab
sector, the government sector, the banking
sector, and the foreign sector. Another button
is linked to the introductory tutorials on causal links and feedback loops. The two colorful
buttons at the bottom are links to the “simulation labs” where control buttons, time series
graphs, and various options are available for using the model. The simulation experiments
MacroLab: The Interactive Learning Environment 78
are conducted on the Experimental Lab
page, where the time series graphs display
only the behavior of the model and not
historical data. The Historical Lab page is
used for either viewing historical time series
data for the US economy, or for comparing
the historical performance of the US
economy and the performance of
MacroLab. Such a comparison makes sense
only when MacroLab is running in historic
mode.
On both simulation lab pages, the user
can click a switch to make the model run in
either experimental or historic mode. The
default option is experimental mode, and
Figure 67. Overview
“re-set” buttons restore all default options.
The mode choice depends on whether the
user’s purpose is to see how the model
behaves under various parameter or structural assumptions, (in which case, the experimental
mode would typically be selected) or whether the purpose is to see how the model’s behavior
compares with actual historical behavior of the US economy.
The main functional distinction between the two modes is the way the stocks are
initialized. In experimental mode, the stocks always have the same initial values. In historic
mode, stocks take on the initial values that existed in the particular historical year in which
the simulation begins (e.g., 1986 or 1993), and the model is simulated from that initial
disequilibrium state. After the simulation begins in historic mode, stocks change
endogenously based on the same equations used in the experimental mode. The foreign
submodel does not function in historic mode; instead, the US sector relies on historical
exogenous values for U.S. imports, exports, and net capital flows.
The large button labeled “The Issue” is a recent addition to the Overview page and, as
such, it is linked to a page that is still under construction. In the spirit of the admonition to
model problems and not systems, a modification-in-progress is the establishment of a
“problem” that will provide focus to the study of the economic system during the
macroeconomics course. Tentatively, the level of employment (or the rate of unemployment)
has been selected as “the issue.” Getting a job and remaining gainfully employed is an issue
of relevance to most students. Moreover, studying the way that jobs are created (and
destroyed) requires consideration of a host of relationships in the economy. In other words,
using the issue of employment as the searchlight for exploring the economy, students will
discover much about the way the entire economic system is structured. Moreover, the
relationships uncovered will help construct (or renovate) students’ mental models of the US
economy. Finally, such a focus enables a start-small-and-build-out approach to learning. An
extended study of the causes and effects of employment (and the unemployment rate) will
inevitably intersect with such topics as GDP, inflation, interest rates, exchange rates, taxes,
and government spending. However, the context of those topics will be more obvious when
MacroLab: The Interactive Learning Environment 79
the fundamental question is always: “How does that relate to employment?” The Issue page
should be fully functional by the 2007 summer semester.
2. Historical Lab
Figure 68 displays the Historical Lab page. Note that the experimental mode switch is
ON (“green”). The default population growth rate is zero in experimental mode, which is
why the red labor force line is flat on the graph. The pink curve, on the other hand, traces the
growth of the actual US labor force stock over the twenty-year period since 1986. If the user
wanted to see the model’s projection of the labor force over that time period, then the historic
mode switch should be ON. Note, however, that a few additional settings are necessary
before the model will be ready to run in historic mode, and those settings require going to the
Experimental Lab. After that, the user would return to the Historical Lab to run the
simulation and view the results. Turning the pages of the graph will reveal additional
historical time series data and corresponding model estimates for the same variables.
Figure 68. Historical Lab (in experimental mode)
The time period of the simulation is selected by clicking the “simulation settings”
button. As Figure 69 shows, there are many other options available, but most users of the
model should change only the “From” and “To” dates. When historic mode is operational,
pick the desired calendar year period for the simulation length. When in experimental mode,
the length of the simulation depends on the user’s purpose. If the primary purpose is to view
short-run changes in unemployment, for example, a simulation period “from” 0 “to” 10 years
might be a good choice. That would be long enough to observe at least one and maybe two
inventory cycles but not so long that the interesting variations were compressed too tightly to
be discernible. On the other hand, significant changes in the stock of capital would require a
longer simulation period.
MacroLab: The Interactive Learning Environment 80
It is important, however, to remember
that MacroLab is primarily a short-term
business cycle model.
When in
experimental mode, a simulation length that
spanned many decades or a century might
be technically possible (i.e., the model
would run without “exploding”), but the
results would be misleading. The constant
value assumptions for many exogenous
parameters in the model would be incorrect
over such long time periods.
More
importantly, some key real-world structure
Figure 69. Simulation Settings: Users Should
could be different in distant time periods,
Change Only the Length of the Simulation
but the model’s structure would remain the
same. Floating exchange rates became the
norm only in the mid-1970s, for example. Also, prior to the 1950s, the Federal Reserve
System was part of the Treasury Department and lacked the independence of modern central
banks. Moreover, when the model is running in historic mode, there could be an additional
problem. It is recommended that simulation periods not begin earlier than 1980 because not
all historical stocks in the model’s current database contain data for years prior to that date.
The model might appear to run satisfactorily from, say, 1950, but hidden from the user’s view
might be the fact that a certain historical stock was not initialized accurately.
Before leaving the Historical Lab page, it is worth repeating the distinction between
Historical Lab and historic mode. In the Historical Lab, users see actual historical data on the
time series graphs, regardless of which mode (experimental or historic) is operating. In
historic mode, the model is trying to replicate the actual historic behavior of the US economy.
It does so by beginning the simulation with the same conditions that existed at that "time" in
US history. For example, if the simulation began in 1990, the initial values for the money
supply, employment, interest rates, etc., would be the actual values that existed in 1990.
After that initial beginning, however, the behavior of the model would depend on all the
relationships in the model. It would not
keep using actual data throughout the
simulation. In experimental mode, the
model depends on the same structural
relationships as in historic mode, but the
initial values are set by default in the
model (e.g., initial employment = 100
million persons) or by the user (e.g., price
adjustment time). Figure 70 illustrates an
historic mode simulation, in which
Figure 70. Historic Mode Simulation, 1996-2006
MacroLab tracks the historical
Historical (light blue) & Simulated (dark blue)
unemployment rate closely until the two
Unemployment Rate
patterns diverge near the end of the
simulation period.
MacroLab: The Interactive Learning Environment 81
3. Experimental Lab
Figure 71 displays the Experimental Lab page, and the experimental mode is ON. The
unique feature of the Experimental Lab page is the user capability to select the structure of
the economy and many parameter values before (and during) a simulation. The simple
Private Sector is always ON (“green”) and cannot be turned OFF. By default, the
Government and Banking sectors turn ON when the re-set button is clicked, but either or both
may be turned OFF. The default condition of the Foreign sector is OFF. The Foreign sector
should not be ON unless both the Government and Banking sectors are also ON. The pulldown menu on the Experimental Lab page (Figure 72) provides users with dozens of
opportunities to examine the implications for behavior when parameter assumptions are
changed.
Figure 71. Experimental Lab
The user also has the exogenous
power to “shock” the model and observe
the behavior patterns that emerge. Clicking
“money supply rise,” for example, causes a
sudden $40 billion injection of reserves into
the commercial banking system.
The
“consumption drop” switch causes a sudden
reduction in consumers’ propensity to spend
(and increases their propensity to save),
amounting to about 2 percent of disposable
income. These and other switches enable
putting the model economy into a simulated
Figure 72. Pull-Down Menu Provides Options
for Changing Parameter Assumptions
MacroLab: The Interactive Learning Environment 82
recession or expansion. Following the shock of a money supply increase, for example, the
unemployment rate oscillates relatively more when price adjustments occur relatively slowly
(Figure 73).
Before doing the simulation experiment in Figure 73, students would be required to
study the feedback loop structure in Figure 74. They would do some “thought experiments”
about the effect on employment if prices were “sticky”; i.e., if prices adjusted slowly to
sudden changes in demand (up or down). In the threaded discussion board for the distance
learning course, they would post their hypotheses for the behavior of loop C1. Then they
would be assigned a simulation exercise, such as the one in Figure 73, in order to “test drive”
their hypotheses.
Figure 73. Experimental Mode Simulation of
Unemployment after Money Supply Rises
Figure 74. Possible “Sticky Price” Loop, C1
4. Sector Tutorials
From the Overview page, the user
can link to sections within the ILE that
correspond to the structural sectors in the
model economy: simple private sector,
government sector, banking sector, and
foreign sector. The page for each of those
sectors is similar in layout, and Figure 75
displays the page for the Demand (i.e.,
nominal) side of the simple private sector.
The large buttons in the top half of
the page are text buttons with information
for students to read. The bottom half
contains buttons that can display different
views of the private demand side of the
model economy. The “Intro to Demand
Side” button, for example, opens a slide
show that illustrates a set of feedback
Figure 75. ILE Page for Demand Side
MacroLab: The Interactive Learning Environment 83
loops, one at a time with
annotation. The “preview” button
on the right provides a one-slide
summary (Figure 76). The other
four small buttons on the page in
Figure 75 actually take the students
to the model layer and display an
unfolding, annotated picture of the
stock-and-flow structure for
different submodels on the private
demand side. Each of the other
sector tutorial pages is similar to
this one, in terms of layout and
function.
5. Final Comments
This version of the interactive
learning environment will be the
Figure 76. The Preview of the Private Demand Side
nucleus for a future electronic
textbook version of MacroLab that
will be accessible via the Internet. The highest priority for the next phase is interactive
hypothesis development with “coaching” from the ILE. The fundamental objective will
remain the same—to improve learning the dynamics of an economy by studying its feedback
structure.
MacroLab: The Interactive Learning Environment 84
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